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A122657
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a(n) = if n mod 2 = 1 then (n^2-1)*n^3/4 else n^5/4.
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3
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0, 0, 8, 54, 256, 750, 1944, 4116, 8192, 14580, 25000, 39930, 62208, 92274, 134456, 189000, 262144, 353736, 472392, 617310, 800000, 1018710, 1288408, 1606044, 1990656, 2437500, 2970344, 3582306, 4302592, 5121690, 6075000, 7149840, 8388608, 9774864, 11358856
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OFFSET
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0,3
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COMMENTS
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Wiener index of product of two cycles of length n.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (2,3,-8,-2,12,-2,-8,3,2,-1).
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FORMULA
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G.f.: 2*x^2*(4*x^6+19*x^5+62*x^4+70*x^3+62*x^2+19*x+4) /((x+1)^4*(x-1)^6). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 28 2009
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MATHEMATICA
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Table[If[Mod[n, 2] == 0, n^5, (n^2 - 1) n^3]/4, {n, 0, 20}] (* Eric W. Weisstein, May 10 2017 *)
LinearRecurrence[{2, 3, -8, -2, 12, -2, -8, 3, 2, -1}, {0, 8, 54, 256,
CoefficientList[Series[2 x^2 (4 x^6 + 19 x^5 + 62 x^4 + 70 x^3 + 62 x^2 + 19 x + 4)/((x + 1)^4 (x - 1)^6), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 08 2017 *)
If[OddQ[#], ((#^2-1)#^3)/4, #^5/4]&/@Range[0, 40] (* Harvey P. Dale, Jul 03 2021 *)
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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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