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

0,5

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

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

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 *)

Crossrefs

Sequence in context: A321309 A023608 A218189 * A018087 A171625 A284245

Adjacent sequences: A132777 A132778 A132779 * A132781 A132782 A132783

Keyword

nonn

Author

Paul Curtz, Nov 17 2007

Extensions

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

Status

approved