OFFSET
2,3
COMMENTS
In general (2^n/m)*Sum_{r=0..m-1} cos(2*Pi*k*r/m)*cos(2*Pi*r/m)^n is the number of walks of length n between two nodes at distance k in the cycle graph C_m. Here we have m=9 and k=2.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,5,-4,-5,2).
FORMULA
a(n) = (2^n/9)*Sum_{r=0..8} cos(4*Pi*r/9)*cos(2*Pi*r/9)^n.
G.f.: x^2(-1+x+x^2)/((1+x)*(-1+2x)*(1-3x^2+x^3));
a(n) = a(n-1) + 5*a(n-2) - 4*a(n-3) - 5*a(n-4) + 2*a(n-5).
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Herbert Kociemba, Jul 03 2004
STATUS
approved