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Number of closed walks on C_5 tensor J_2.
1

%I #10 Mar 08 2021 12:41:06

%S 1,0,4,0,48,32,640,896,8960,18432,130048,337920,1941504,5857280,

%T 29605888,98435072,458424320,1624375296,7174881280,26507476992,

%U 113123524608,429538672640,1792440008704,6929367695360,28495396732928

%N Number of closed walks on C_5 tensor J_2.

%C Let (C_5 tensor J_2) be the 10 node graph whose adjacency matrix is the tensor product of that of C_5 and J_2=[1,1;1,1]. Then a(n) counts closed walks of length n at a vertex of the graph.

%D E.R. van Dam, Graphs with few eigenvalues, Tilburg, 1968, p53.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,12,-16).

%F G.f.: (1-2x-8x^2+8x^3)/((1-4x)(1+2x-4x^2)); a(n)=2a(n-1)+12a(n-2)-16a(n-3), n>4; a(n)=(sqrt(5)-1)^n/5+(-sqrt(5)-1)^n/5+4^n/10+0^n/2.

%F (1/10) [4^n - (-2)^(n+1)*Lucas(n) ], n>0. - _Ralf Stephan_, May 16 2007

%F a(n)= 2^n*A052964(n-2), n>0. - _R. J. Mathar_, Mar 08 2021

%Y Cf. A101501.

%K easy,nonn

%O 0,3

%A _Paul Barry_, Dec 04 2004