A145133 - OEIS

%I #9 Jul 31 2015 21:41:53

%S 0,1,5,15,35,71,132,231,386,622,974,1491,2241,3318,4852,7023,10080,

%T 14367,20359,28712,40332,56470,78853,109865,152797,212192,294321,

%U 407840,564697,781384,1080665,1493961,2064642,2852571,3940376,5442107,7515185

%N Expansion of x/((1 - x - x^4)*(1 - x)^4).

%C The coefficients of the recursion for a(n) are given by the 5th row of A145152.

%H Harvey P. Dale, <a href="/A145133/b145133.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 (5, -10, 10, -4, -3, 6, -4, 1).

%F a(n) = 5a(n-1) -10a(n-2) +10a(n-3) -4a(n-4) -3a(n-5) +6a(n-6) -4a(n-7) +a(n-8).

%e a(9) = 622 = 5*386 -10*231 +10*132 -4*71 -3*35 +6*15 -4*5 +1.

%p col:= proc(k) local l, j, M, n; l:= `if` (k=0, [1, 0, 0, 1], [seq (coeff ( -(1-x-x^4) *(1-x)^(k-1), x, j), j=1..k+3)]); M:= Matrix (nops(l), (i,j)-> if i=j-1 then 1 elif j=1 then l[i] else 0 fi); `if` (k=0, n->(M^n)[2,3], n->(M^n)[1,2]) end: a:= col(5): seq (a(n), n=0..40);

%t CoefficientList[Series[x/((1-x-x^4)*(1-x)^4),{x,0,40}],x] (* or *) LinearRecurrence[{5,-10,10,-4,-3,6,-4,1},{0,1,5,15,35,71,132,231},40] (* _Harvey P. Dale_, Oct 24 2011 *)

%o (PARI) Vec(1/((1 - x - x^4)*(1 - x)^4)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 24 2012

%Y 5th column of A145153. Cf. A145152.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Oct 03 2008