A076149 Expansion of x^2(3+2x)/(1-x-5x^2-3x^3).

0, 3, 5, 20, 54, 169, 499, 1506, 4508, 13535, 40593, 121792, 365362, 1096101, 3288287, 9864878, 29594616, 88783867, 266351581, 799054764, 2397164270, 7191492833, 21574478475, 64723435450, 194170306324, 582510918999

Offset

1,2

Comments

Let b(1)=x, b(2)=y, k*b(k)=(2k-1)*b(k-1) + 3(k+1)*b(k-2); then b(n)=c(n)*x+a(n)/3*y.

Links

Table of n, a(n) for n=1..26.

Formula

a(1)=0; a(n+1) = 3*a(n)-(-1)^n*(n+2); a(n)=floor((11/48)*3^n+(-1)^n*n/4+1/2)

Mathematica

CoefficientList[Series[x^2(3+2x)/(1-x-5x^2-3x^3), {x, 0, 30}], x] (* Harvey P. Dale, Nov 23 2018 *)

Prog

(PARI) a(n)=if(n<0, 0, polcoeff(x^2*(3+2*x)/(1-x-5*x^2-3*x^3)+x*O(x^n), n))

Crossrefs

Sequence in context: A261116 A295361 A295357 * A133102 A197156 A171864

Adjacent sequences: A076146 A076147 A076148 * A076150 A076151 A076152

Keyword

nonn

Author

Benoit Cloitre, Nov 02 2002

Status

approved