A113727 A Pell convolution.

1, 0, 4, 4, 17, 32, 88, 200, 497, 1184, 2876, 6924, 16737, 40384, 97520, 235408, 568353, 1372096, 3312564, 7997204, 19306993, 46611168, 112529352, 271669848, 655869073, 1583407968, 3822685036, 9228778012, 22280241089, 53789260160

Offset

0,3

Comments

Convolution of A000129(n+1) and (n+1)*(-1)^n.

Links

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (0,4,4,1).

Formula

G.f.: 1/((1-2x-x^2)(1+2x+x^2)); a(n)=4a(n-2)+4a(n-3)+a(n-4); a(n)=sum{k=0..floor(n/2), C(n-k, k)2^(n-2k)*(1+(-1)^(n-k))/2}.

a(n) = A000129(n+1)/2 +(n+1)*(-1)^n/2. - R. J. Mathar, Sep 20 2012

Mathematica

LinearRecurrence[{0, 4, 4, 1}, {1, 0, 4, 4}, 30] (* Harvey P. Dale, May 24 2014 *)

Crossrefs

Cf. A094686, A113726.

Sequence in context: A294245 A117785 A117787 * A214141 A193961 A368197

Adjacent sequences: A113724 A113725 A113726 * A113728 A113729 A113730

Keyword

easy,nonn

Author

Paul Barry, Nov 08 2005

Status

approved