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

Author

Paul Barry, Nov 08 2005

Keywords

• easy
• nonn

Comments

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,1,4,4).

Crossrefs

Cf. A094686, A089977, A001045, A001607.

Programs

Mathematica

LinearRecurrence[{0,1,4,4},{1,0,1,4},40] (* Harvey P. Dale, Apr 30 2025 *)

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