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A056520
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a(n) = (n + 2)*(2*n^2 - n + 3)/6.
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18
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1, 2, 6, 15, 31, 56, 92, 141, 205, 286, 386, 507, 651, 820, 1016, 1241, 1497, 1786, 2110, 2471, 2871, 3312, 3796, 4325, 4901, 5526, 6202, 6931, 7715, 8556, 9456, 10417, 11441, 12530, 13686, 14911, 16207, 17576, 19020, 20541, 22141, 23822
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OFFSET
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0,2
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COMMENTS
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Equals (1, 2, 3, 4, 5, ...) convolved with (1, 0, 3, 5, 7, 9, ...). - Gary W. Adamson, Jul 31 2010
a(n) equals n!^2 times the determinant of the n X n matrix whose (i,j)-entry is 1 + KroneckerDelta[i, j] (-1 + (1 + i^2)/i^2). - John M. Campbell, May 20 2011
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LINKS
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FORMULA
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a(n) = a(n-1) + n^2.
G.f.: (1 - 2*x + 4*x^2 - x^3)/(1 - x)^4. - Paul Barry, Apr 14 2010
Let b(0) = b(1) = 1, b(n) = max(b(n-1) + (n - 1)^2, b(n-2) + (n - 2)^2) for n >= 2; then a(n) = b(n+1). - Yalcin Aktar, Jul 28 2011
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MATHEMATICA
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s = 1; lst = {s}; Do[s += n^2; AppendTo[lst, s], {n, 1, 41, 1}]; lst (* Zerinvary Lajos, Jul 12 2009 *)
Table[n!^2*Det[Array[KroneckerDelta[#1, #2](((#1^2+1)/(#1^2))-1)+1&, {n, n}]], {n, 1, 20}] (* John M. Campbell, May 20 2011 *)
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PROG
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CROSSREFS
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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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