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%I #12 Jan 23 2022 15:21:52
%S 1,1,6,7,28,36,120,165,495,716,2003,3018,8024,12512,31977,51357,
%T 127110,209475,504736,850840,2003784,3445885,7956715,13926276,
%U 31609071,56191734,125640180,226444616,499685777,911607609,1988440598
%N Number of walks of length n between two nodes at distance 4 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=4.
%H Michael De Vlieger, <a href="/A095369/b095369.txt">Table of n, a(n) for n = 4..3325</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,5,-4,-5,2).
%F a(n) = (2^n/9)*Sum_{r=0..8} cos(8*Pi*r/9)*cos(2*Pi*r/9)^n.
%F G.f.: x^4/((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).
%t 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 *)
%K nonn,easy
%O 4,3
%A _Herbert Kociemba_, Jul 03 2004
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