A078058 Expansion of (1-x)/(1+2*x-x^2+x^3).

1, -3, 7, -18, 46, -117, 298, -759, 1933, -4923, 12538, -31932, 81325, -207120, 527497, -1343439, 3421495, -8713926, 22192786, -56520993, 143948698, -366611175, 933692041, -2377943955, 6056191126, -15424018248, 39282171577, -100044552528, 254795294881, -648917313867

Offset

0,2

Comments

a(n) is the upper left entry of the n-th power of the 3 X 3 matrix M = [-3, -3, 1; 1, 1, 0; 1, 0, 0]; a(n) = M^n [1, 1]. - Philippe Deléham, Apr 19 2023

Links

Table of n, a(n) for n=0..29.

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

Formula

a(n) = -2*a(n-1) + a(n-2) - a(n-3) for n > 2; a(0) = 1, a(1) = -3, a(2) = 7. - Harvey P. Dale, Oct 22 2011

a(n) = Sum_{k = 0..n} A188316(n, k)*(-3)^k. - Philippe Deléham, Apr 19 2023

Mathematica

CoefficientList[Series[(1-x)/(1+2x-x^2+x^3), {x, 0, 30}], x] (* or *) LinearRecurrence[{-2, 1, -1}, {1, -3, 7}, 31] (* Harvey P. Dale, Oct 22 2011 *)

Prog

(PARI) Vec((1-x)/(1+2*x-x^2+x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

Crossrefs

Sequence in context: A191826 A318899 A114713 * A116413 A052960 A059512

Adjacent sequences: A078055 A078056 A078057 * A078059 A078060 A078061

Keyword

sign,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved