A087629 Generalized Jacobsthal sequence.

1, 1, 3, 2, 11, 21, 22, 85, 171, 170, 683, 1365, 1366, 5461, 10923, 10922, 43691, 87381, 87382, 349525, 699051, 699050, 2796203, 5592405, 5592406, 22369621, 44739243, 44739242, 178956971, 357913941, 357913942, 1431655765, 2863311531

Offset

0,3

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-2k), 3)=0, comb(n, k), 0) }; a(3n)=A001045(3n+1)-A001045(3n); a(3n+1)=A001045(3n+2), a(3n+2)=A001045(3n+3).

G.f.: (4x^4-5x^3+3x^2+x+1)/(-8x^6-7x^3+1).

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

Crossrefs

Cf. A087628.

Sequence in context: A116391 A305491 A358589 * A254214 A362995 A178384

Adjacent sequences: A087626 A087627 A087628 * A087630 A087631 A087632

Keyword

easy,nonn

Author

Paul Barry, Sep 14 2003

Status

approved