A113726 A Jacobsthal convolution.

1, 0, 1, 4, 5, 8, 25, 44, 77, 176, 353, 660, 1365, 2776, 5417, 10876, 21981, 43648, 87153, 175076, 349669, 698280, 1398585, 2797260, 5590381, 11184720, 22373761, 44735284, 89474165, 178969208, 357910345, 715807004, 1431683837, 2863325216

Offset

0,4

Comments

Convolution of A001045(n+1) and A001607(n+1).

Links

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

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

Formula

G.f.: 1/((1-x-2*x^2)*(1+x+2*x^2)).

a(n) = a(n-2) + 4*a(n-3) + 4*a(n-4).

a(n) = Sum_{k=0..floor(n/2)} C(n-k, k)*2^k*(1+(-1)^(n-k))/2.

a(n) = 2^n/3 + (-1)^n/6 + A001607(n+1)/2. - R. J. Mathar, Aug 23 2011

a(n) = sum(A128099(n, n-2*k), k=0..floor(n/2)). - Johannes W. Meijer, Aug 28 2013

Crossrefs

Cf. A094686, A089977, A001045, A001607.

Sequence in context: A072808 A104884 A226795 * A207191 A240790 A229861

Adjacent sequences: A113723 A113724 A113725 * A113727 A113728 A113729

Keyword

easy,nonn,changed

Author

Paul Barry, Nov 08 2005

Status

approved