OFFSET
0,2
COMMENTS
Number of walks of length 2n on the 6-regular tree beginning and ending at some fixed vertex. Hankel transform is A135349. - Philippe Deléham, Feb 25 2009
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
a(n) = Sum_{k=0..n} A039599(n,k)*5^(n-k). - Philippe Deléham, Aug 25 2007
From Gary W. Adamson, Jul 22 2011: (Start)
a(n) = upper left term in M^n, M = an infinite square production matrix as follows:
6, 6, 0, 0, 0, 0, ...
5, 5, 5, 0, 0, 0, ...
5, 5, 5, 5, 0, 0, ...
5, 5, 5, 5, 5, 0, ...
5, 5, 5, 5, 5, 5, ...
... (End)
D-finite with recurrence: n*a(n) = 2*(28*n-15)*a(n-1) - 360*(2*n-3)*a(n-2). - Vaclav Kotesovec, Oct 20 2012
a(n) ~ 3*2^(2*n-3)*5^(n+1)/(sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 20 2012
MATHEMATICA
CoefficientList[Series[5/(2+3*Sqrt[1-20*x]), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 20 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Philippe Deléham, Aug 23 2007
EXTENSIONS
More terms from Olivier Gérard, Sep 22 2007
STATUS
approved