A317200 Expansion of g.f. -x*(2*x^3+2*x^2+x-2)/(x^4-2*x+1).

0, 2, 3, 4, 6, 10, 17, 30, 54, 98, 179, 328, 602, 1106, 2033, 3738, 6874, 12642, 23251, 42764, 78654, 144666, 266081, 489398, 900142, 1655618, 3045155, 5600912, 10301682, 18947746, 34850337, 64099762, 117897842, 216847938, 398845539, 733591316, 1349284790, 2481721642

Offset: 1

Author

N. J. A. Sloane, Aug 05 2018

Keywords

• nonn
• easy

Comments

a(n) = length of A317199(n).

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000
• Bo Tan and Zhi-Ying Wen, Some properties of the Tribonacci sequence, European Journal of Combinatorics, 28 (2007) 1703-1719. See Prop. 2.9.
• Index entries for linear recurrences with constant coefficients, signature (2,0,0,-1).

Crossrefs

Cf. A000073, A317199.

Programs

Mathematica

CoefficientList[Series[-x(2x^3+2x^2+x-2)/(x^4-2x+1),{x,0,40}],x] (* Harvey P. Dale, Aug 31 2020 *)

PARI

my(N=40); Vec(x*(2 - x - 2*x^2 - 2*x^3)/((1 - x)*(1 - x - x^2 - x^3)) + O(x^N), -N) \\ Andrew Howroyd, Oct 24 2023

Formula

Bo Tan et al. express a(n) in terms of the tribonacci numbers A000073.

Extensions

Zero prepended by Harvey P. Dale, Aug 31 2020

a(36)-a(38) from Stefano Spezia, Oct 24 2023