%I #9 Jun 23 2015 05:43:39

%S 1,3,6,10,15,21,28,36,44,52,60,68,76,84,92,100,109,119,130,142,155,

%T 169,184,200,216,232,248,264,280,296,312,328,345,363,382,402,423,445,

%U 468,492,516,540,564,588,612,636,660,684,709,735,762,790,819,849,880,912

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

%C Triangular numbers A000217 start: 0,1,3,6,10,15,21,28,36,45,55

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1, 0, 0, 0, 0, -1, 3, -3, 1).

%F a(0)=1, a(1)=3, a(2)=6, a(3)=10, a(4)=15, a(5)=21, a(6)=28, a(7)=36, a(8)=44, a(9)=52, a(10)=60, a(n)=3*a(n-1)-3*a(n-2)+a(n-3)-a(n-8)+ 3*a(n-9)- 3*a(n-10)+a (n-11). - _Harvey P. Dale_, Jan 28 2015

%p seriestolist(series(1/((x^8+1)*(x-1)^3), x=0,100));

%t CoefficientList[Series[1/((1-x)^3 (1+x^8)),{x,0,60}],x] (* or *) LinearRecurrence[{3,-3,1,0,0,0,0,-1,3,-3,1},{1,3,6,10,15,21,28,36,44,52,60},60] (* _Harvey P. Dale_, Jan 28 2015 *)

%Y Cf. A000217.

%K easy,nonn

%O 0,2

%A _Creighton Dement_, Jul 17 2005

%E Definition corrected by _Harvey P. Dale_, Jan 28 2015