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a(n) = floor((n+1)*(n-3)*(n-4)/12).
1

%I #25 Nov 16 2024 20:06:18

%S 1,1,0,0,0,1,3,8,15,25,38,56,78,105,137,176,221,273,332,400,476,561,

%T 655,760,875,1001,1138,1288,1450,1625,1813,2016,2233,2465,2712,2976,

%U 3256,3553,3867,4200,4551,4921,5310,5720,6150,6601,7073,7568,8085,8625,9188,9776,10388,11025,11687,12376,13091,13833,14602,15400,16226

%N a(n) = floor((n+1)*(n-3)*(n-4)/12).

%H Vincenzo Librandi, <a href="/A212772/b212772.txt">Table of n, a(n) for n = 0..1000</a>

%H Dominique BĂ©nard, <a href="https://doi.org/10.1016/0095-8956(78)90074-6">Orientable imbedding of line graphs</a>, J. Combinatorial Theory Ser. B 24 (1978), no. 1, 34--43. MR0485482(58 #5312)

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,1,-3,3,-1).

%F G.f.: (1-2*x+2*x^3-2*x^4+3*x^5)/((1+x+x^2+x^3)*(1-x)^4). [_Bruno Berselli_, May 26 2012]

%F a(n) = 1+(2*(n-5)*(n-1)*n-3*(1+(-1)^n)*(1-i^((n-1)*n)))/24, where i=sqrt(-1). [_Bruno Berselli_, May 26 2012]

%t Table[Floor[(n + 1) (n - 3) ((n - 4)/12)], {n, 0, 60}] (* _Bruno Berselli_, May 26 2012 *)

%o (Magma) m:=61; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-2*x+2*x^3-2*x^4+3*x^5)/((1+x+x^2+x^3)*(1-x)^4))); // _Bruno Berselli_, May 26 2012

%o (Maxima) makelist(1+(2*(n-5)*(n-1)*n-3*(1+(-1)^n)*(1-%i^((n-1)*n)))/24, n, 0, 60); /* _Bruno Berselli_, May 26 2012 */

%K nonn,easy

%O 0,7

%A _N. J. A. Sloane_, May 26 2012