A151575 G.f.: (1+x)/(1+x-2*x^2).

1, 0, 2, -2, 6, -10, 22, -42, 86, -170, 342, -682, 1366, -2730, 5462, -10922, 21846, -43690, 87382, -174762, 349526, -699050, 1398102, -2796202, 5592406, -11184810, 22369622, -44739242, 89478486, -178956970, 357913942, -715827882, 1431655766, -2863311530, 5726623062

Offset

0,3

Comments

Or, g.f. = (1+x)/((1-x)*(1-2*x)).

A signed version of A078008, which is the main entry.

[1, 0, 2, -2, 6, -10, 22, -42, 86, ...] = an operator for toothpick sequences. The sequence convolved with A151548 = toothpick sequence A139250. The sequence convolved with A151555 = toothpick sequence A153006. - Gary W. Adamson, May 25 2009

Links

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (-1,2).

Formula

From R. J. Mathar, Jul 08 2009: (Start)

a(n) = (2 + (-2)^n)/3 = (-1)^n*A078008(n), n>=0.

a(n) = 2*A077925(n-2), n>1. (End)

a(n) = A084247(n+1)/2. - Philippe Deléham, Sep 21 2009

G.f.: 1 + x - x*Q(0), where Q(k) = 1 + 2*x^2 - (2*k+3)*x + x*(2*k+1 - 2*x)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 05 2013

Mathematica

CoefficientList[Series[(1+x)/(1+x-2x^2), {x, 0, 40}], x] (* or *) LinearRecurrence[{-1, 2}, {1, 0}, 40] (* Harvey P. Dale, May 31 2023 *)

Crossrefs

Cf. A078008, A077925, A084247.

Cf. A139250, A151548, A151555.

Sequence in context: A300274 A019310 A078008 * A014113 A284462 A262278

Adjacent sequences: A151572 A151573 A151574 * A151576 A151577 A151578

Keyword

sign

Author

N. J. A. Sloane, May 25 2009, based on a suggestion from Gary W. Adamson

Status

approved