A095308 Number of walks of length n between two nodes at distance 3 in the cycle graph C_7.

1, 1, 5, 6, 21, 28, 84, 121, 331, 507, 1300, 2093, 5110, 8568, 20129, 34885, 79477, 141494, 314489, 572264, 1246784, 2309385, 4950751, 9303411, 19684692, 37427313, 78354346, 150402700, 312168761, 603861897, 1244620149

Offset: 3

Author

Herbert Kociemba, Jul 03 2004

Keywords

• nonn

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).

Crossrefs

Partial sums of A095307.

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).