OFFSET
0,4
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 walks of length n between adjacent vertices of this 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.: x(1-2x)/((1-4x)(1+2x-4x^2)); a(n)=2a(n-1)+12a(n-2)-16a(n-3); a(n)=(sqrt(5)-1)^(n+1)/20-(sqrt(5)+1)^(n+1)(-1)^n/20+4^n/10; a(n)=sum{k=0..n, sqrt(5)((sqrt(5)-1)^k/10-(-sqrt(5)-1)^k/10)(4^(n-k)+0^(n-k))/2}.
(1/10) [4^n - (-2)^n*Lucas(n+1) ]. - Ralf Stephan, May 16 2007
a(n) = 2^(n-1)*A052964(n-1). - R. J. Mathar, Mar 08 2021
MATHEMATICA
LinearRecurrence[{2, 12, -16}, {0, 1, 0}, 30] (* Harvey P. Dale, Apr 09 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Dec 04 2004
STATUS
approved