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

Author

Paul Barry, Nov 08 2005

Keywords

• easy
• nonn

Comments

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

Links

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

Crossrefs

Cf. A094686, A113726.

Programs

Mathematica

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

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