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A173549
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Number of 3 X 3 magilatin squares with positive values and magic sum n.
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8
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12, 12, 24, 72, 156, 240, 552, 600, 1020, 1548, 2004, 2568, 4008, 4644, 6264, 8136, 10152, 12168, 16284, 18372, 22992, 27972, 32736, 37896, 47352, 52332, 62004, 72288, 82572, 93108, 110280, 120492, 138420, 157428, 175248, 193824, 223428
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OFFSET
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6,1
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COMMENTS
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A magilatin square has equal row and column sums and no number repeated in any row or column.
a(n) is given by a quasipolynomial of degree 4 and period 840.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (-2, -3, -2, 0, 3, 6, 8, 9, 7, 3, -4, -10, -15, -16, -14, -8, 0, 8, 14, 16, 15, 10, 4, -3, -7, -9, -8, -6, -3, 0, 2, 3, 2, 1).
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FORMULA
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G.f.: x^3/(1-x^3) * { 12*x^3/[(x-1)*(x^2-1)] - 108*x^5/[(x-1)*(x^2-1)^2] - 72*x^5/[(x-1)*(x^4-1)] - 72*x^5/[(x^3-1)*(x^2-1)] - 36*x^5/(x^5-1) + 72*x^7/[(x-1)*(x^2-1)^3] + 144*x^7/[(x-1)*(x^2-1)*(x^4-1)] + 72*x^7/[(x-1)*(x^6-1)] + 72*x^7/[(x^2-1)^2*(x^3-1)] + 72*x^7/[(x^2-1)*(x^5-1)] + 72*x^7/(x^7-1) + 72*x^9/[(x-1)*(x^4-1)^2] + 144*x^9/[(x^2-1)*(x^3-1)*(x^4-1)] + 144*x^9/[(x^3-1)*(x^6-1)] + 72*x^9/[(x^4-1)*(x^5-1)] + 72*x^11/[(x^3-1)*(x^4-1)^2] + 72*x^11/[(x^3-1)*(x^8-1)] + 72*x^11/[(x^5-1)*(x^6-1)] + 72*x^13/[(x^5-1)*(x^8-1)] }.
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MATHEMATICA
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LinearRecurrence[{-2, -3, -2, 0, 3, 6, 8, 9, 7, 3, -4, -10, -15, -16, -14, -8, 0, 8, 14, 16, 15, 10, 4, -3, -7, -9, -8, -6, -3, 0, 2, 3, 2, 1}, {0, 0, 0, 0, 0, 12, 12, 24, 72, 156, 240, 552, 600, 1020, 1548, 2004, 2568, 4008, 4644, 6264, 8136, 10152, 12168, 16284, 18372, 22992, 27972, 32736, 37896, 47352, 52332, 62004, 72288, 82572}, 42][[6;; ]] (* Jean-François Alcover, Nov 06 2018 *)
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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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