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A276159
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Convolution of nonzero octagonal numbers (A000567) with themselves.
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0
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1, 16, 106, 416, 1211, 2912, 6132, 11712, 20757, 34672, 55198, 84448, 124943, 179648, 252008, 345984, 466089, 617424, 805714, 1037344, 1319395, 1659680, 2066780, 2550080, 3119805, 3787056, 4563846, 5463136, 6498871, 7686016, 9040592, 10579712, 12321617, 14285712, 16492602, 18964128
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OFFSET
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0,2
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LINKS
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FORMULA
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O.g.f.: (1 + 5*x)^2/(1 - x)^6.
E.g.f.: (30 + 450*x + 1125*x^2 + 725*x^3 + 150*x^4 + 9*x^5)*exp(x)/30.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).
a(n) = (n + 1)*(n + 2)*(n + 3)*(9*n^2 + 6*n + 5)/30.
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MATHEMATICA
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LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 16, 106, 416, 1211, 2912}, 36]
Table[(n + 1) (n + 2) (n + 3) ((9 n^2 + 6 n + 5)/30), {n, 0, 35}]
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CROSSREFS
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Cf. similar sequences of the convolution of k-gonal numbers with themselves listed in A271662.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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