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A194478
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Number of ways to arrange 6 indistinguishable points on an n X n X n triangular grid so that no three points are in the same row or diagonal.
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1
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0, 0, 0, 1, 337, 8733, 96478, 668028, 3413828, 14054915, 49171641, 151422970, 420674150, 1073422309, 2550004472, 5699074284, 12082541388, 24462528078, 47555986746, 89173692795, 161899772067, 285517344145, 490447009030
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OFFSET
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1,5
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LINKS
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FORMULA
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a(n) = (1/256)*(-1)^n*(2*n - 7)*(n^2 - 7*n + 13) + (1/322560)*(7*n^12 + 42*n^11 - 945*n^10 + 1274*n^9 + 26089*n^8 - 128810*n^7 + 175693*n^6 + 205366*n^5 - 810796*n^4 + 601328*n^3 + 354172*n^2 - 582180*n + 114660).
Recurrence: (n-2)*(14*n^11 + 70*n^10 - 2051*n^9 + 5299*n^8 + 50106*n^7 - 359946*n^6 + 953463*n^5 - 1085555*n^4 - 364412*n^3 + 3593716*n^2 - 6028304*n + 3620736)*a(n+2) + (-126*n^11 - 966*n^10 + 13377*n^9 + 4662*n^8 - 354550*n^7 + 1123664*n^6 - 1113309*n^5 + 85056*n^4 + 1719696*n^3 - 7286000*n^2 + 10210192*n - 3854400)*a(n+1) - (n+2)*(14*n^11 + 224*n^10 - 581*n^9 - 7700*n^8 + 31682*n^7 - 11948*n^6 - 91561*n^5 + 168104*n^4 - 482042*n^3 + 1253272*n^2 - 1293160*n + 383136)*a(n) = 0. (End)
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EXAMPLE
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Some solutions for 5 X 5 X 5:
0 0 1 0 0 1 1
0 0 1 0 0 0 1 1 1 0 0 0 0 1
1 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1 0 0
0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 0 1 0 1 0 1 1 0 0 0 1 0
1 0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 1 0
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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