OFFSET
1,2
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
S. Butler and R. Graham, Enumerating (multiplex) juggling sequences, arXiv:0801.2597 [math.CO], 2008.
Index entries for linear recurrences with constant coefficients, signature (9,-21,13).
FORMULA
G.f.: (x-6*x^2+7*x^3)/(1-9*x+21*x^2-13*x^3).
From Colin Barker, Aug 31 2016: (Start)
a(n) = (13+(4-sqrt(3))^n*(4+sqrt(3))-(-4+sqrt(3))*(4+sqrt(3))^n)/39.
a(n) = 9*a(n-1)-21*a(n-2)+13*a(n-3) for n>3.
(End)
EXAMPLE
a(2)=3 since <3> -> <2,1> -> <3>; <3> -> <1,2> -> <3> and <3> -> <0,3> -> <3> are the three possibilities.
PROG
(PARI) Vec((x-6*x^2+7*x^3)/(1-9*x+21*x^2-13*x^3) + O(x^30)) \\ Colin Barker, Aug 31 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Steve Butler, Jan 21 2008
STATUS
approved