A135019 a(n) = -a(n-1) + 2*a(n-2) - a(n-3), with a(0) = 0, a(1) = 1, a(2) = -3.

0, 1, -3, 5, -12, 25, -54, 116, -249, 535, -1149, 2468, -5301, 11386, -24456, 52529, -112827, 242341, -520524, 1118033, -2401422, 5158012, -11078889, 23796335, -51112125, 109783684, -235804269, 506483762, -1087875984, 2336647777, -5018883507, 10780055045, -23154469836

Offset

0,3

Comments

Sequence is identical to its signed second differences less first 3 terms. - R. J. Mathar, May 17 2009

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

From R. J. Mathar, May 17 2009: (Start)

a(n)*(-1)^(n+1) = A002478(n-1) + 2*A002478(n-2).

G.f.: x*(1 - 2*x)/(1 + x - 2*x^2 + x^3). (End)

Mathematica

LinearRecurrence[{-1, 2, -1}, {0, 1, -3}, 35] (* Paolo Xausa, Jun 03 2026 *)

Prog

(PARI) a(n)=([0, 1, 0; 0, 0, 1; -1, 2, -1]^n*[0; 1; -3])[1, 1] \\ Charles R Greathouse IV, Jun 03 2026

Crossrefs

Cf. A002478.

Sequence in context: A030270 A129757 A141685 * A017921 A280000 A241097

Adjacent sequences: A135016 A135017 A135018 * A135020 A135021 A135022

Keyword

sign,easy

Author

Paul Curtz, Feb 10 2008

Extensions

More terms from R. J. Mathar, May 17 2009

Status

approved