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%I #9 Sep 10 2019 02:37:07
%S 1,0,4,0,15,1,56,9,210,56,792,299,3003,1470,11441,6868,43776,31008,
%T 168151,136629,648208,591261,2507046,2523676,9726080,10656387,
%U 37839375,44612702,147600981,185477216,577147212,766744608,2261792303
%N Number of walks of length n between two nodes at distance 2 in the cycle graph C_9.
%C 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.
%F a(n) = (2^n/9)*Sum_{r=0..8} cos(4*Pi*r/9)*cos(2*Pi*r/9)^n).
%F G.f.: x^2(-1+x+x^2)/((1+x)*(-1+2x)*(1-3x^2+x^3));
%F a(n) = a(n-1) + 5*a(n-2) - 4*a(n-3) - 5*a(n-4) + 2*a(n-5).
%K nonn
%O 2,3
%A _Herbert Kociemba_, Jul 03 2004
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