A289296 revision #19
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A289296
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a(n) = (n - 1)*(2*floor(n/2) + 1).
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4
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-1, 0, 3, 6, 15, 20, 35, 42, 63, 72, 99, 110, 143, 156, 195, 210, 255, 272, 323, 342, 399, 420, 483, 506, 575, 600, 675, 702, 783, 812, 899, 930, 1023, 1056, 1155, 1190, 1295, 1332, 1443, 1482, 1599, 1640, 1763, 1806, 1935, 1980, 2115, 2162, 2303, 2352, 2499, 2550, 2703, 2756, 2915
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OFFSET
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0,3
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COMMENTS
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Summing a(n) by pairs, one gets -1, 9, 35, 77, 135, ... = A033566.
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LINKS
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FORMULA
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a(n) = n^2-1 if n is even and n^2-n if n is odd.
G.f.: -(1 - x - 5*x^2 - x^3 - 2*x^4) / ((1 - x)^3*(1 + x)^2).
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>4. (End)
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MATHEMATICA
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Table[(n - 1) (2 Floor[n/2] + 1), {n, 0, 60}] (* or *) LinearRecurrence[{1, 2, -2, -1, 1}, {-1, 0, 3, 6, 15}, 61]
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PROG
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(PARI) Vec(-(1 - x - 5*x^2 - x^3 - 2*x^4) / ((1 - x)^3*(1 + x)^2) + O(x^60)) \\ Colin Barker, Jul 02 2017
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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proposed
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