A285197 Expansion of (1-6*x+11*x^2-5*x^3) / ((1-x)*(1-3*x)*(1-3*x+x^2)).

1, 1, 2, 6, 20, 67, 221, 717, 2294, 7258, 22760, 70863, 219353, 675769, 2073674, 6342414, 19345052, 58867195, 178779893, 542042565, 1641058046, 4962262306, 14989121072, 45235277511, 136407241265, 411058035697, 1237981634066, 3726531171222, 11212544793764, 33723901952563

Offset: 0

Author

N. J. A. Sloane, Apr 30 2017

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• M. H. Albert, M. D. Atkinson, and V. Vatter, Inflations of geometric grid classes: three case studies, arXiv:1209.0425 [math.CO], 2012.
• Index entries for linear recurrences with constant coefficients, signature (7,-16,13,-3).

Crossrefs

Cf. A262600.

Programs

Mathematica

LinearRecurrence[{7,-16,13,-3},{1,1,2,6},30] (* Harvey P. Dale, Apr 01 2018 *)

PARI

Vec((1-6*x+11*x^2-5*x^3) / ((1-x)*(1-3*x)*(1-3*x+x^2)) + O(x^30)) \\ Colin Barker, May 01 2017

Formula

From Colin Barker, May 01 2017: (Start)

a(n) = 7*a(n-1) - 16*a(n-2) + 13*a(n-3) - 3*a(n-4) for n>3.

a(n) = (1/2 + 3^n/2 + (2^(-n)*((3-sqrt(5))^n - (3+sqrt(5))^n)) / sqrt(5)).

(End)

2*a(n) = 1 +3^n -2*A001906(n). - R. J. Mathar, Aug 19 2022