A077873 Expansion of (1-x)^(-1)/(1-x+x^2+2*x^3).

1, 2, 2, -1, -6, -8, 1, 22, 38, 15, -66, -156, -119, 170, 602, 671, -270, -2144, -3215, -530, 6974, 13935, 8022, -19860, -55751, -51934, 43538, 206975, 267306, -26744, -707999, -1215866, -454378, 2177487, 5063598, 3794868, -5623703, -19545766, -21511798, 9281375, 69884706, 103626928

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..510

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

Formula

a(n) = 2*a(n-4)-a(n-3)-2*a(n-2)+2*a(n-1). - Robert Israel, May 19 2014

Maple

N:= 100; # to get a(n) for n <= N
A:= <<0, 1, 0, 0>|<0, 0, 1, 0>|<0, 0, 0, 1>|<2, -1, -2, 2>>:
seq(<1|2|2|-1> . A^j . <1, 0, 0, 0>, j=0..N); # Robert Israel, May 19 2014

Mathematica

CoefficientList[Series[(1-x)^(-1)/(1-x+x^2+2x^3), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, -2, -1, 2}, {1, 2, 2, -1}, 50] (* Harvey P. Dale, Jul 21 2025 *)

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; 2, -1, -2, 2]^n*[1; 2; 2; -1])[1, 1] \\ Charles R Greathouse IV, Jun 02 2026

Crossrefs

Sequence in context: A343847 A135880 A380204 * A123305 A118024 A184184

Adjacent sequences: A077870 A077871 A077872 * A077874 A077875 A077876

Keyword

sign,easy,changed

Author

N. J. A. Sloane, Nov 17 2002

Status

approved