OFFSET
3,3
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=7 and k=3.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1, 4, -3, -2).
FORMULA
a(n) = (2^n/7)*Sum_{r=0..6} cos(6*Pi*r/7)*cos(2*Pi*r/7)^n.
G.f.: x^3/((-1 + 2x)*(-1 - x + 2x^2 + x^3)).
a(n) = a(n-1) + 4*a(n-2) - 3*a(n-3) - 2*a(n-4).
CROSSREFS
KEYWORD
nonn
AUTHOR
Herbert Kociemba, Jul 03 2004
STATUS
approved