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A095367 Number of walks of length n between two nodes at distance 2 in the cycle graph C_9. 0
1, 0, 4, 0, 15, 1, 56, 9, 210, 56, 792, 299, 3003, 1470, 11441, 6868, 43776, 31008, 168151, 136629, 648208, 591261, 2507046, 2523676, 9726080, 10656387, 37839375, 44612702, 147600981, 185477216, 577147212, 766744608, 2261792303 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=2..34.

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

Sequence in context: A006710 A141150 A081162 * A060052 A059065 A170771

Adjacent sequences:  A095364 A095365 A095366 * A095368 A095369 A095370

KEYWORD

nonn

AUTHOR

Herbert Kociemba, Jul 03 2004

STATUS

approved

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Last modified July 31 19:55 EDT 2021. Contains 346377 sequences. (Running on oeis4.)