OFFSET
1,1
COMMENTS
This is trace of A^n where A is adjacency matrix of the kite graph (K4 with one edge deleted).
REFERENCES
Godsil, Algebraic Combinatorics, Chapman & Hall, Inc, 1993, pages 22-23
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,5,4).
FORMULA
Generating function in terms of characteristic polynomial from Godsil (1993) is 2*x*(2 - 5*x^2 - 2*x^3) / ((1 + x)*(1 - x - 4*x^2)).
From Colin Barker, Dec 25 2017: (Start)
a(n) = 2^(-3-n) * ((-1)^(1+n)*2^(3+n) - (1-sqrt(17))^n*(1+sqrt(17)) + (-1+sqrt(17))*(1+sqrt(17))^n) for n>1.
a(n) = 5*a(n-2) + 4*a(n-3) for n>4.
(End)
MATHEMATICA
Series[2*x*(2 - 5*x^2 - 2*x^3) / ((1 + x)*(1 - x - 4*x^2)), {x, 0, 20}][[3]]
PROG
(PARI) Vec(2*x*(2 - 5*x^2 - 2*x^3) / ((1 + x)*(1 - x - 4*x^2)) + O(x^40)) \\ Colin Barker, Dec 25 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Yaroslav Bulatov (yaroslavvb(AT)gmail.com), Nov 02 2010
STATUS
approved