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A285197
Expansion of (1-6*x+11*x^2-5*x^3) / ((1-x)*(1-3*x)*(1-3*x+x^2)).
1
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
0,3
LINKS
M. H. Albert, M. D. Atkinson, and V. Vatter, Inflations of geometric grid classes: three case studies, arXiv:1209.0425 [math.CO], 2012.
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
MATHEMATICA
LinearRecurrence[{7, -16, 13, -3}, {1, 1, 2, 6}, 30] (* Harvey P. Dale, Apr 01 2018 *)
PROG
(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
CROSSREFS
Cf. A262600.
Sequence in context: A226510 A108627 A193234 * A372872 A148475 A148476
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 30 2017
STATUS
approved