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A095308
Number of walks of length n between two nodes at distance 3 in the cycle graph C_7.
1
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
3,3
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.
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
Partial sums of A095307.
Sequence in context: A057520 A060423 A037951 * A132796 A006492 A110344
KEYWORD
nonn
AUTHOR
Herbert Kociemba, Jul 03 2004
STATUS
approved