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A135258 Inverse binomial transform of A131666 after removing A131666(0) = 0. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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).

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

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A113405.

Sequence in context: A308092 A262765 A131666 * A034065 A034075 A281716

Adjacent sequences:  A135255 A135256 A135257 * A135259 A135260 A135261

KEYWORD

sign

AUTHOR

Paul Curtz, Dec 01 2007

EXTENSIONS

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

STATUS

approved

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Last modified July 10 15:45 EDT 2020. Contains 335577 sequences. (Running on oeis4.)