OFFSET
0,3
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).
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 30 2017
STATUS
approved