A037236 Expansion of (3+2*x^2)/(1-x)^4.

3, 12, 32, 68, 125, 208, 322, 472, 663, 900, 1188, 1532, 1937, 2408, 2950, 3568, 4267, 5052, 5928, 6900, 7973, 9152, 10442, 11848, 13375, 15028, 16812, 18732, 20793, 23000, 25358, 27872, 30547, 33388

Offset

0,1

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n)= (n+1)*(5*n^2+13*n+18)/6. a(n)= 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - R. J. Mathar, Feb 12 2010

Mathematica

CoefficientList[Series[(3+2x^2)/(1-x)^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {3, 12, 32, 68}, 40] (* Harvey P. Dale, Apr 09 2018 *)

Prog

(PARI) a(n)=(n+1)*(5*n^2+13*n+18)/6 \\ Charles R Greathouse IV, Oct 19 2022

Crossrefs

Sequence in context: A005718 A199231 A098500 * A309693 A365738 A288605

Adjacent sequences: A037233 A037234 A037235 * A037237 A037238 A037239

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved