A140403 - OEIS

%I #17 May 31 2018 06:04:58

%S 0,0,0,0,8,24,32,56,72,96,128,160,192,232,272,320,368,424,472,536,600,

%T 664,736,808,880,968,1048,1136,1224,1320,1416,1520,1624,1728,1840,

%U 1960,2072,2200,2320,2448,2584,2720,2856,3000,3144,3296,3448,3608,3760,3928,4096

%N Expansion of 8*x^4/((1-x)^2*(1-x^3)) + 8*x^5/((1-x)*(1-x^2)*(1-x^5)).

%H Harvey P. Dale, <a href="/A140403/b140403.txt">Table of n, a(n) for n = 0..1000</a>

%H Guoce Xin, <a href="https://doi.org/10.1016/j.disc.2007.06.022">Constructing all magic squares of order three</a>, Discrete Math., 308 (2008), 3393-3398.

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,0,0,0,-1,-1,0,1).

%F a(0)=0, a(1)=0, a(2)=0, a(3)=0, a(4)=8, a(5)=24, a(6)=32, a(7)=56, a(8)=72, a(9)=96, a(n)=a(n-2)+a(n-3)-a(n-7)-a(n-8)+a(n-10). [_Harvey P. Dale_, Mar 22 2012]

%F a(n) = 8*A140402(n). - _R. J. Mathar_, Sep 27 2014

%t CoefficientList[Series[8x^4/((1-x)^2(1-x^3))+8x^5/((1-x)(1-x^2)(1-x^5)),{x,0,60}],x] (* or *) LinearRecurrence[{0,1,1,0,0,0,-1,-1,0,1},{0,0,0,0,8,24,32,56,72,96},60] (* _Harvey P. Dale_, Mar 22 2012 *)

%K nonn,easy

%O 0,5

%A _N. J. A. Sloane_, Jun 20 2008