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%I #14 May 04 2017 08:25:07
%S 0,0,0,0,1,5,15,34,68,120,200,310,465,665,931,1260,1680,2184,2808,
%T 3540,4425,5445,6655,8030,9636,11440,13520,15834,18473,21385,24675,
%U 28280,32320,36720,41616,46920,52785,59109,66063,73530,81700,90440,99960,110110,121121
%N a(n) = binomial(n,4) - binomial(floor(n/2),4) - binomial(ceiling(n/2),4).
%H Colin Barker, <a href="/A111385/b111385.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-6,0,6,-2,-2,1).
%F a(n) = +2 a(n-1) +2 a(n-2) -6 a(n-3) +6 a(n-5) -2 a(n-6) -2 a(n-7) +a(n-8). - _R. J. Mathar_, Mar 11 2012
%F G.f.: x^4*(1 + 3*x + 3*x^2) / ((1 - x)^5*(1 + x)^3). - _Colin Barker_, Jul 28 2013
%F From _Colin Barker_, May 04 2017: (Start)
%F a(n) = n^2 * (7*n^2 - 36*n + 44) / 192 for n even.
%F a(n) = (7*n^4 - 36*n^3 + 38*n^2 + 36*n - 45) / 192 for n odd.
%F (End)
%o (PARI) concat(vector(4), Vec(x^4*(1 + 3*x + 3*x^2) / ((1 - x)^5*(1 + x)^3) + O(x^60))) \\ _Colin Barker_, May 04 2017
%K nonn,easy
%O 0,6
%A _N. J. A. Sloane_, Nov 10 2005
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