OFFSET
0,3
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).
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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Dec 04 2004
STATUS
approved