A132780 a(0)=1. a(n+1)=2*a(n)-A130151(n).

1, 1, 1, 1, 3, 7, 15, 29, 57, 113, 227, 455, 911, 1821, 3641, 7281, 14563, 29127, 58255, 116509, 233017, 466033, 932067, 1864135, 3728271, 7456541, 14913081, 29826161, 59652323, 119304647, 238609295, 477218589, 954437177, 1908874353, 3817748707

Offset: 0

Author

Paul Curtz, Nov 17 2007

Keywords

• nonn

Comments

The first member of the sequences of the d'-th differences (that is, the diagonal of the pyramidal arrangement of repeated differences and essentially the binomial transform of 2*A113405) has the same absolute value as the first differences themselves, cf. the comment in A113405.

Links

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

Programs

Mathematica

nxt[{n_,a_}]:={n+1,If[MemberQ[{1,2,3},Mod[n+1,6]],2a-1,2a+1]}; NestList[ nxt, {0,1},40][[All,2]] (* Harvey P. Dale, Jul 06 2019 *)

Formula

First differences: a(n+1)-a(n)= 2*A113405(n).

O.g.f.: (1-x-x^2)/((1+x)(1-x+x^2)(1-2x)). - R. J. Mathar, Jul 16 2008

Extensions

Edited and extended by R. J. Mathar, Jul 16 2008