A077887 Expansion of (1-x)^(-1)/(1+x^2-2*x^3).

1, 1, 0, 2, 3, -1, 2, 8, -3, -3, 20, -2, -25, 43, 22, -92, 65, 137, -248, -6, 523, -489, -534, 1536, -443, -2603, 3516, 1718, -8721, 5315, 12158, -22756, -1527, 47073, -43984, -50126, 138131, -37841, -238382, 314104, 162701, -790867, 465508, 1116270, -2047241, -185253, 4279782, -3909228

Offset

0,4

Links

Table of n, a(n) for n=0..47.

Index entries for linear recurrences with constant coefficients, signature (1,-1,3,-2).

Formula

a(n) = a(n-1) - a(n-2) + 3 a(n-3) - 2 a(n-4), with a(0) = a(1) = 1, a(2) = 0 and a(3) = 2. - Jean-François Alcover, Apr 06 2016

a(n) = n+1 - a(n-1) - 2*a(n-2), with a(0) = a(1) = 1. - Michel Marcus, Apr 06 2016

Mathematica

RecurrenceTable[{a[1] == a[2] == 1, a[n] == n - a[n-1] - 2 a[n-2]}, a, {n, 50}] (* Jean-François Alcover, Apr 06 2016 *)
LinearRecurrence[{1, -1, 3, -2}, {1, 1, 0, 2}, 50] (* Harvey P. Dale, Sep 14 2019 *)

Prog

(PARI) Vec(1/((1-x)*(1+x^2-2*x^3)) + O(x^60)) \\ Michel Marcus, Apr 06 2016

Crossrefs

Sequence in context: A209557 A183759 A101477 * A059379 A065487 A341287

Adjacent sequences: A077884 A077885 A077886 * A077888 A077889 A077890

Keyword

sign,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved