OFFSET
4,3
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=4.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 4..3325
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(8*Pi*r/9)*cos(2*Pi*r/9)^n.
G.f.: x^4/((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).
MATHEMATICA
Drop[CoefficientList[Series[-x^4/((1 + x) (-1 + 2 x) (1 - 3 x^2 + x^3)), {x, 0, 34}], x], 4] (* Michael De Vlieger, Jan 23 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Herbert Kociemba, Jul 03 2004
STATUS
approved