login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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