A103819 Whitney transform of Jacobsthal numbers.

0, 1, 3, 8, 23, 63, 172, 471, 1287, 3516, 9607, 26247, 71708, 195911, 535239, 1462300, 3995079, 10914759, 29819676, 81468871, 222577095, 608091932, 1661338055, 4538859975, 12400396060, 33878512071, 92557816263, 252872656668

Offset

0,3

Comments

The Whitney transform maps the sequence with g.f. g(x) to that with g.f. (1/(1-x))*g(x(1+x)).

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,2,1,-2,-2).

Formula

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

a(n) = 2a(n-1)+2a(n-2)+a(n-3)-2a(n-4)-2a(n-5).

a(n) = Sum_{k=0..n} Sum_{i=0..n} C(k, i-k)*A001045(k).

9*a(n) = -2 +2*(A002605(n)+2*A002605(n+1))-A099837(n+3). - R. J. Mathar, Oct 23 2011

Mathematica

LinearRecurrence[{2, 2, 1, -2, -2}, {0, 1, 3, 8, 23}, 30] (* Harvey P. Dale, Nov 02 2024 *)

Crossrefs

Cf. A004070, A001045, A002605, A099837.

Sequence in context: A261329 A375468 A248870 * A147484 A316980 A331321

Adjacent sequences: A103816 A103817 A103818 * A103820 A103821 A103822

Keyword

easy,nonn

Author

Paul Barry, Feb 16 2005

Status

approved