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A113726 A Jacobsthal convolution. 2
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 (list; graph; refs; listen; history; text; internal format)
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.

Sequence in context: A072808 A104884 A226795 * A207191 A240790 A229861

Adjacent sequences:  A113723 A113724 A113725 * A113727 A113728 A113729

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Nov 08 2005

STATUS

approved

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Last modified April 20 14:27 EDT 2019. Contains 322310 sequences. (Running on oeis4.)