A101502 Number of closed walks on C_5 tensor J_2.

1, 0, 4, 0, 48, 32, 640, 896, 8960, 18432, 130048, 337920, 1941504, 5857280, 29605888, 98435072, 458424320, 1624375296, 7174881280, 26507476992, 113123524608, 429538672640, 1792440008704, 6929367695360, 28495396732928

Offset: 0

Author

Paul Barry, Dec 04 2004

Keywords

• easy
• nonn

Comments

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.

References

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

Links

• Index entries for linear recurrences with constant coefficients, signature (2,12,-16).

Crossrefs

Cf. A101501.

Formula

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.

(1/10) [4^n - (-2)^(n+1)*Lucas(n) ], n>0. - Ralf Stephan, May 16 2007

a(n)= 2^n*A052964(n-2), n>0. - R. J. Mathar, Mar 08 2021