A087628 Generalized Jacobsthal sequence.

1, 2, 2, 2, 10, 22, 22, 86, 170, 170, 682, 1366, 1366, 5462, 10922, 10922, 43690, 87382, 87382, 349526, 699050, 699050, 2796202, 5592406, 5592406, 22369622, 44739242, 44739242, 178956970, 357913942, 357913942, 1431655766, 2863311530

Offset

0,2

Links

Table of n, a(n) for n=0..32.

Index entries for linear recurrences with constant coefficients, signature (0,0,7,0,0,8).

Formula

a(n)=sum{k=0..n, if (mod(k(n-k), 3)=0, comb(n, k), 0) }; a(n)=if (mod(n, 3)=0, A001045(n+1)-A001045(n), A001045(n+1)-(-1)^n).

G.f.: ( -1-2*x-2*x^2+5*x^3+4*x^4-8*x^5 ) / ( (2*x-1)*(1+x)*(4*x^2+2*x+1)*(x^2-x+1) ). - R. J. Mathar, Dec 10 2014

Crossrefs

Cf. A087629.

Sequence in context: A353261 A291666 A122946 * A263060 A089871 A236046

Adjacent sequences: A087625 A087626 A087627 * A087629 A087630 A087631

Keyword

easy,nonn

Author

Paul Barry, Sep 14 2003

Status

approved