OFFSET
0,3
COMMENTS
Greater of number of closed walks of length n from a node on a pentagon and number of walks of length n between two adjacent nodes on a pentagon.
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,3,-6,-1,2).
FORMULA
a(n) = 2*a(n-1)+3*a(n-2)-6*a(n-3)-a(n-4)+2*a(n-5). - Colin Barker, Sep 14 2014
G.f.: -(x-1)*(x^3+3*x^2-1) / ((2*x-1)*(x^2-x-1)*(x^2+x-1)). - Colin Barker, Sep 14 2014
EXAMPLE
For n=15, k=7 mod 5 gives k=2, 7 or 12, and C(15,2)+C(15,7)+C(15,12) = 105+6435+455, so a(15)=6995.
PROG
(PARI) Vec(-(x-1)*(x^3+3*x^2-1)/((2*x-1)*(x^2-x-1)*(x^2+x-1)) + O(x^100)) \\ Colin Barker, Sep 14 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, Feb 10 2010
STATUS
approved