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

Table of n, a(n) for n=0..27.

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

Crossrefs

Cf. A004070, A001045.

Sequence in context: A146998 A261329 A248870 * A147484 A316980 A331321

Adjacent sequences: A103816 A103817 A103818 * A103820 A103821 A103822

Keyword

easy,nonn

Author

Paul Barry, Feb 16 2005

Status

approved