By the request of OP (Alexander Bagdasaryan) I put some more answer here :
I write the answer with format like this :
[a,b,c,d,e,f,g,h,i],[j,k,l,m,n,o,p,q,r]
means :
the magic-square: the alpha magic square
a b c j k l
d e f m n o
g h i p q r
Some of the solutions are :
[119,213,16,13,116,219,216,19,113],[15,16,11,10,14,18,17,12,13]
[113,219,16,19,116,213,216,13,119],[13,18,11,12,14,16,17,10,15]
[124,210,17,10,117,224,217,24,110],[17,12,10,6,13,20,16,14,9]
[120,214,17,14,117,220,217,20,114],[11,18,10,12,13,14,16,8,15]
[114,220,17,20,117,214,217,14,120],[15,14,10,8,13,18,16,12,11]
[110,224,17,24,117,210,217,10,124],[9,20,10,14,13,12,16,6,17]
[124,212,18,12,118,224,218,24,112],[17,16,12,10,15,20,18,14,13]
[112,224,18,24,118,212,218,12,124],[13,20,12,14,15,16,18,10,17]
[135,205,20,5,120,235,220,35,105],[15,10,8,4,11,18,14,12,7]
[105,235,20,35,120,205,220,5,135],[7,18,8,12,11,10,14,4,15]
[129,213,21,13,121,229,221,29,113],[17,16,12,10,15,20,18,14,13]
[126,216,21,16,121,226,221,26,116],[16,17,12,11,15,19,18,13,14]
[116,226,21,26,121,216,221,16,126],[14,19,12,13,15,17,18,11,16]
[113,229,21,29,121,213,221,13,129],[13,20,12,14,15,16,18,10,17]
[131,213,22,13,122,231,222,31,113],[15,16,11,10,14,18,17,12,13]
[127,217,22,17,122,227,222,27,117],[15,16,11,10,14,18,17,12,13]
[117,227,22,27,122,217,222,17,127],[13,18,11,12,14,16,17,10,15]
[113,231,22,31,122,213,222,13,131],[13,18,11,12,14,16,17,10,15]
[131,215,23,15,123,231,223,31,115],[15,16,11,10,14,18,17,12,13]
[115,231,23,31,123,215,223,15,131],[13,18,11,12,14,16,17,10,15]
[138,212,25,12,125,238,225,38,112],[17,16,12,10,15,20,18,14,13]
[112,238,25,38,125,212,225,12,138],[13,20,12,14,15,16,18,10,17]
[138,214,26,14,126,238,226,38,114],[17,18,13,12,16,20,19,14,15]
[134,218,26,18,126,234,226,34,118],[17,18,13,12,16,20,19,14,15]
[118,234,26,34,126,218,226,18,134],[15,20,13,14,16,18,19,12,17]
[114,238,26,38,126,214,226,14,138],[15,20,13,14,16,18,19,12,17]
[139,215,27,15,127,239,227,39,115],[17,16,12,10,15,20,18,14,13]
[115,239,27,39,127,215,227,15,139],[13,20,12,14,15,16,18,10,17]
[157,203,30,3,130,257,230,57,103],[16,9,8,3,11,19,14,13,6]
[153,207,30,7,130,253,230,53,107],[15,10,8,4,11,18,14,12,7]
[107,253,30,53,130,207,230,7,153],[7,18,8,12,11,10,14,4,15]
[103,257,30,57,130,203,230,3,157],[6,19,8,13,11,9,14,3,16]
[151,211,31,11,131,251,231,51,111],[16,17,12,11,15,19,18,13,14]
[111,251,31,51,131,211,231,11,151],[14,19,12,13,15,17,18,11,16]
[152,212,32,12,132,252,232,52,112],[15,16,11,10,14,18,17,12,13]
[146,218,32,18,132,246,232,46,118],[13,18,11,12,14,16,17,10,15]
[118,246,32,46,132,218,232,18,146],[15,16,11,10,14,18,17,12,13]
[112,252,32,52,132,212,232,12,152],[13,18,11,12,14,16,17,10,15]
[153,213,33,13,133,253,233,53,113],[15,16,11,10,14,18,17,12,13]
[113,253,33,53,133,213,233,13,153],[13,18,11,12,14,16,17,10,15]
[146,224,35,24,135,246,235,46,124],[13,20,12,14,15,16,18,10,17]
[144,226,35,26,135,244,235,44,126],[14,19,12,13,15,17,18,11,16]
[126,244,35,44,135,226,235,26,144],[16,17,12,11,15,19,18,13,14]
[124,246,35,46,135,224,235,24,146],[17,16,12,10,15,20,18,14,13]
[163,211,37,11,137,263,237,63,111],[16,17,12,11,15,19,18,13,14]
[161,213,37,13,137,261,237,61,113],[17,16,12,10,15,20,18,14,13]
[151,223,37,23,137,251,237,51,123],[16,17,12,11,15,19,18,13,14]
[148,226,37,26,137,248,237,48,126],[14,19,12,13,15,17,18,11,16]
[146,228,37,28,137,246,237,46,128],[13,20,12,14,15,16,18,10,17]
[128,246,37,46,137,228,237,28,146],[17,16,12,10,15,20,18,14,13]
[126,248,37,48,137,226,237,26,148],[16,17,12,11,15,19,18,13,14]
[123,251,37,51,137,223,237,23,151],[14,19,12,13,15,17,18,11,16]
[113,261,37,61,137,213,237,13,161],[13,20,12,14,15,16,18,10,17]
[111,263,37,63,137,211,237,11,163],[14,19,12,13,15,17,18,11,16]
[164,214,39,14,139,264,239,64,114],[19,18,14,12,17,22,20,16,15]
[114,264,39,64,139,214,239,14,164],[15,22,14,16,17,18,20,12,19]
[173,215,44,15,144,273,244,73,115],[15,16,11,10,14,18,17,12,13]
[115,273,44,73,144,215,244,15,173],[13,18,11,12,14,16,17,10,15]
[183,207,45,7,145,283,245,83,107],[17,10,9,4,12,20,15,14,7]
[160,230,45,30,145,260,245,60,130],[13,14,9,8,12,16,15,10,11]
[130,260,45,60,145,230,245,30,160],[11,16,9,10,12,14,15,8,13]
[107,283,45,83,145,207,245,7,183],[7,20,9,14,12,10,15,4,17]
[189,203,46,3,146,289,246,89,103],[20,9,10,3,13,23,16,17,6]
[183,209,46,9,146,283,246,83,109],[17,12,10,6,13,20,16,14,9]
[182,210,46,10,146,282,246,82,110],[17,12,10,6,13,20,16,14,9]
[172,220,46,20,146,272,246,72,120],[15,14,10,8,13,18,16,12,11]
[170,222,46,22,146,270,246,70,122],[12,17,10,11,13,15,16,9,14]
[122,270,46,70,146,222,246,22,170],[14,15,10,9,13,17,16,11,12]
[120,272,46,72,146,220,246,20,172],[11,18,10,12,13,14,16,8,15]
[110,282,46,82,146,210,246,10,182],[9,20,10,14,13,12,16,6,17]
[109,283,46,83,146,209,246,9,183],[9,20,10,14,13,12,16,6,17]
[103,289,46,89,146,203,246,3,189],[6,23,10,17,13,9,16,3,20]
[186,210,48,10,148,286,248,86,110],[19,12,11,6,14,22,17,16,9]
[170,226,48,26,148,270,248,70,126],[12,19,11,13,14,15,17,9,16]
[155,241,48,41,148,255,248,55,141],[16,15,11,9,14,19,17,13,12]
[151,245,48,45,148,251,248,51,145],[16,15,11,9,14,19,17,13,12]
[145,251,48,51,148,245,248,45,151],[12,19,11,13,14,15,17,9,16]
[141,255,48,55,148,241,248,41,155],[12,19,11,13,14,15,17,9,16]
[126,270,48,70,148,226,248,26,170],[16,15,11,9,14,19,17,13,12]
[110,286,48,86,148,210,248,10,186],[9,22,11,16,14,12,17,6,19]
[157,241,49,41,149,257,249,57,141],[16,15,11,9,14,19,17,13,12]
[152,246,49,46,149,252,249,52,146],[15,16,11,10,14,18,17,12,13]
[151,247,49,47,149,251,249,51,147],[16,15,11,9,14,19,17,13,12]
[147,251,49,51,149,247,249,47,151],[12,19,11,13,14,15,17,9,16]
[146,252,49,52,149,246,249,46,152],[13,18,11,12,14,16,17,10,15]
[141,257,49,57,149,241,249,41,157],[12,19,11,13,14,15,17,9,16]
[183,219,51,19,151,283,251,83,119],[17,18,13,12,16,20,19,14,15]
[165,251,37,23,151,279,265,51,137],[17,19,12,11,16,21,20,13,15]
[179,223,51,23,151,279,251,79,123],[18,17,13,11,16,21,19,15,14]
[173,229,51,29,151,273,251,73,129],[15,20,13,14,16,18,19,12,17]
[167,235,51,35,151,267,251,67,135],[17,18,13,12,16,20,19,14,15]
[165,237,51,37,151,265,251,65,137],[17,18,13,12,16,20,19,14,15]
[158,244,51,44,151,258,251,58,144],[18,17,13,11,16,21,19,15,14]
[154,248,51,48,151,254,251,54,148],[18,17,13,11,16,21,19,15,14]
[137,279,37,51,151,251,265,23,165],[15,21,12,13,16,19,20,11,17]
[148,254,51,54,151,248,251,48,154],[14,21,13,15,16,17,19,11,18]
[144,258,51,58,151,244,251,44,158],[14,21,13,15,16,17,19,11,18]
[137,265,51,65,151,237,251,37,165],[15,20,13,14,16,18,19,12,17]
[135,267,51,67,151,235,251,35,167],[15,20,13,14,16,18,19,12,17]
[129,273,51,73,151,229,251,29,173],[17,18,13,12,16,20,19,14,15]
[123,279,51,79,151,223,251,23,179],[14,21,13,15,16,17,19,11,18]
[119,283,51,83,151,219,251,19,183],[15,20,13,14,16,18,19,12,17]
[171,233,52,33,152,271,252,71,133],[16,17,12,11,15,19,18,13,14]
[155,249,52,49,152,255,252,55,149],[16,17,12,11,15,19,18,13,14]
[149,255,52,55,152,249,252,49,155],[14,19,12,13,15,17,18,11,16]
[133,271,52,71,152,233,252,33,171],[14,19,12,13,15,17,18,11,16]
[195,211,53,11,153,295,253,95,111],[16,17,12,11,15,19,18,13,14]
[186,220,53,20,153,286,253,86,120],[19,14,12,8,15,22,18,16,11]
[180,226,53,26,153,280,253,80,126],[14,19,12,13,15,17,18,11,16]
[164,242,53,42,153,264,253,64,142],[19,14,12,8,15,22,18,16,11]
[162,244,53,44,153,262,253,62,144],[16,17,12,11,15,19,18,13,14]
[157,249,53,49,153,257,253,57,149],[16,17,12,11,15,19,18,13,14]
[149,257,53,57,153,249,253,49,157],[14,19,12,13,15,17,18,11,16]
[144,262,53,62,153,244,253,44,162],[14,19,12,13,15,17,18,11,16]
[142,264,53,64,153,242,253,42,164],[11,22,12,16,15,14,18,8,19]
[126,280,53,80,153,226,253,26,180],[16,17,12,11,15,19,18,13,14]
[120,286,53,86,153,220,253,20,186],[11,22,12,16,15,14,18,8,19]
[111,295,53,95,153,211,253,11,195],[14,19,12,13,15,17,18,11,16]
[169,239,54,39,154,269,254,69,139],[19,20,15,14,18,22,21,16,17]
[139,269,54,69,154,239,254,39,169],[17,22,15,16,18,20,21,14,19]
[199,211,55,11,155,299,255,99,111],[18,17,13,11,16,21,19,15,14]
[196,214,55,14,155,296,255,96,114],[17,18,13,12,16,20,19,14,15]
[194,216,55,16,155,294,255,94,116],[18,17,13,11,16,21,19,15,14]
[187,223,55,23,155,287,255,87,123],[18,17,13,11,16,21,19,15,14]
[183,227,55,27,155,283,255,83,127],[17,18,13,12,16,20,19,14,15]
[178,232,55,32,155,278,255,78,132],[18,17,13,11,16,21,19,15,14]
[172,238,55,38,155,272,255,72,138],[15,20,13,14,16,18,19,12,17]
[166,244,55,44,155,266,255,66,144],[18,17,13,11,16,21,19,15,14]
[144,266,55,66,155,244,255,44,166],[14,21,13,15,16,17,19,11,18]
[138,272,55,72,155,238,255,38,172],[17,18,13,12,16,20,19,14,15]
[132,278,55,78,155,232,255,32,178],[14,21,13,15,16,17,19,11,18]
[127,283,55,83,155,227,255,27,183],[15,20,13,14,16,18,19,12,17]
[123,287,55,87,155,223,255,23,187],[14,21,13,15,16,17,19,11,18]
[116,294,55,94,155,216,255,16,194],[14,21,13,15,16,17,19,11,18]
[114,296,55,96,155,214,255,14,196],[15,20,13,14,16,18,19,12,17]
[111,299,55,99,155,211,255,11,199],[14,21,13,15,16,17,19,11,18]
[198,216,57,16,157,298,257,98,116],[18,17,13,11,16,21,19,15,14]
[196,218,57,18,157,296,257,96,118],[17,18,13,12,16,20,19,14,15]
[183,231,57,31,157,283,257,83,131],[17,18,13,12,16,20,19,14,15]
[181,233,57,33,157,281,257,81,133],[18,17,13,11,16,21,19,15,14]
[166,248,57,48,157,266,257,66,148],[18,17,13,11,16,21,19,15,14]
[161,253,57,53,157,261,257,61,153],[17,18,13,12,16,20,19,14,15]
[153,261,57,61,157,253,257,53,161],[15,20,13,14,16,18,19,12,17]
[148,266,57,66,157,248,257,48,166],[14,21,13,15,16,17,19,11,18]
[133,281,57,81,157,233,257,33,181],[14,21,13,15,16,17,19,11,18]
[131,283,57,83,157,231,257,31,183],[15,20,13,14,16,18,19,12,17]
[118,296,57,96,157,218,257,18,196],[15,20,13,14,16,18,19,12,17]
[116,298,57,98,157,216,257,16,198],[14,21,13,15,16,17,19,11,18]
[169,253,61,53,161,269,261,69,153],[19,18,14,12,17,22,20,16,15]
[163,259,61,59,161,263,261,63,159],[16,21,14,15,17,19,20,13,18]
[159,263,61,63,161,259,261,59,163],[18,19,14,13,17,21,20,15,16]
[153,269,61,69,161,253,261,53,169],[15,22,14,16,17,18,20,12,19]
[194,232,63,32,163,294,263,94,132],[18,17,13,11,16,21,19,15,14]
[192,234,63,34,163,292,263,92,134],[15,20,13,14,16,18,19,12,17]
[178,248,63,48,163,278,263,78,148],[18,17,13,11,16,21,19,15,14]
[148,278,63,78,163,248,263,48,178],[14,21,13,15,16,17,19,11,18]
[134,292,63,92,163,234,263,34,192],[17,18,13,12,16,20,19,14,15]
[132,294,63,94,163,232,263,32,194],[14,21,13,15,16,17,19,11,18]
[194,236,65,36,165,294,265,94,136],[18,19,14,13,17,21,20,15,16]
This is my code in Haskell, but I omit the numbers list length (pjg x = y) to make the listed code not too long, after adding the numbers list your self, just run jaw from the main prompt. (sorry if I write it awfully :), it the result come out quite fast). I limited the numbers from 1 to 300.
import Data.List
ak = [1..300]
jaw = [[[a,b,c,d,e,f,g,h,i],[pjg a,pjg b,pjg c,pjg d,pjg e,pjg f,pjg g,pjg h,pjg i]]|
e <- ak, let s1 = e*3, let s2 = (pjg e) * 3,
d <- ak \\ [e],
let f = s1 - (e+d), f > d, f >= 0, f < 1001, sum [pjg d, pjg e, pjg f] == s2,
(length.nub.sort $ [pjg d, pjg e, pjg f]) == 3,
a <- ak \\ [e,d,f], elem (pjg a) [pjg d, pjg e, pjg f] == False,
let g = s1 - (a+d), g > a, g >= 0, g < 1001, (length.nub.sort $ [a,d,e,f,g]) == 5,
sum [pjg a, pjg d, pjg g] == s2, elem (pjg g) [pjg a, pjg d, pjg e, pjg f] == False,
b <- ak \\ [a,d,e,f,g], let c = s1 - (a+b), c >= 0, c < 1001, sum [pjg a, pjg b, pjg c] == s2,
let h = s1 - (b+e), h >= 0, h < 1001, sum [pjg b, pjg e, pjg h] == s2,
let i = s1 - (c+f), i >= 0, i < 1001, sum [pjg c, pjg f, pjg i] == s2, sum [g,h,i] == s1, sum [pjg g, pjg h, pjg i] == s2,
sum [a,e,i] == s1, sum [g,e,c] == s1,
sum [pjg a,pjg e,pjg i] == s2, sum [pjg g,pjg e,pjg c] == s2,
(length.nub.sort $ [a,b,c,d,e,f,g,h,i]) == 9,
(length.nub.sort $ [pjg a,pjg b,pjg c,pjg d,pjg e,pjg f,pjg g,pjg h,pjg i]) == 9,
True]
-- edit this for the numbers-list-length
pjg 0 = 4
pjg 1 = 4
pjg 3 = 3
...
pjg 1000 = 6