A135258 Inverse binomial transform of A131666 after removing A131666(0) = 0.

0, 1, -1, 2, -3, 7, -14, 29, -57, 114, -227, 455, -910, 1821, -3641, 7282, -14563, 29127, -58254, 116509, -233017, 466034, -932067, 1864135, -3728270, 7456541, -14913081, 29826162, -59652323, 119304647, -238609294, 477218589, -954437177, 1908874354

Offset: 0

Author

Paul Curtz, Dec 01 2007

Keywords

• sign

Comments

The inverse binomial transform generally equals the sequence of first terms of the iterated differences (i.e., equals the diagonal of the arrangement in the standard hand-written display of the differences).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-2,0,1,2).

Crossrefs

Cf. A113405.

Programs

Mathematica

LinearRecurrence[{-2, 0, 1, 2}, {0, 1, -1, 2}, 50] (* G. C. Greubel, Oct 04 2016 *)

PARI

concat(0, Vec(x*(1 + x)/((x^2 +x +1)*(1 +2*x)*(1-x)) + O(x^50))) \\ Michel Marcus, Oct 05 2016

Formula

O.g.f.: x*(1 + x)/((x^2 +x +1)*(1 +2*x)*(1-x)). - R. J. Mathar, Jul 22 2008

a(n) = -2*a(n-1) + a(n-3) + 2*a(n-4). - G. C. Greubel, Oct 04 2016

Extensions

Edited and corrected by R. J. Mathar, Jul 22 2008