A200739 Expansion of (-x^2+5*x-1)/(x^3-x^2+5*x-1).

1, 0, 0, 1, 5, 24, 116, 561, 2713, 13120, 63448, 306833, 1483837, 7175800, 34701996, 167818017, 811563889, 3924703424, 18979771248, 91785716705, 443873515701, 2146561633048, 10380720366244, 50200913713873, 242770409836169, 1174031855833216, 5677589783043784

Offset: 0

Author

Alois P. Heinz, Nov 21 2011

Keywords

• nonn
• easy

Comments

Peter A. Lawrence (see links) has posted a challenge to find a 3x3 integer matrix with "smallish" elements whose powers generate a sequence that is not in the OEIS. This sequence is one of the solutions found.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..450
• Peter Lawrence et al., sequence challenge and follow-up messages on the SeqFan list, Nov 21 2011
• Index entries for linear recurrences with constant coefficients, signature (5,-1,1)

Crossrefs

Cf. A200676.

Programs

Maple

a:= n-> (<<0|1|0>, <0|0|1>, <1|-1|5>>^n)[1, 1]:
seq(a(n), n=0..30);

Mathematica

CoefficientList[Series[(-x^2 + 5 x - 1)/(x^3 - x^2 + 5 x - 1), {x, 0, 30}], x] (* or *) LinearRecurrence[{5,-1,1},{1,0,0},30] (* Harvey P. Dale, Nov 26 2017 *)

Formula

G.f.: (-x^2+5*x-1)/(x^3-x^2+5*x-1).

Term (1,1) in the 3x3 matrix [0,1,0; 0,0,1; 1,-1,5]^n.