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A130977 G.f.: 5/(2+3*sqrt(1-20*x)). 6
1, 6, 66, 876, 12786, 197796, 3183156, 52718616, 892401426, 15368638836, 268388185596, 4741271556456, 84573471344916, 1521119577791976, 27554494253636136, 502257203287150896, 9205363627419463506 (list; graph; refs; listen; history; text; internal format)
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<=k<=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)

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

Column k=6 of A183135.

Sequence in context: A004355 A282046 A124862 * A191096 A151832 A133306

Adjacent sequences:  A130974 A130975 A130976 * A130978 A130979 A130980

KEYWORD

nonn

AUTHOR

Philippe Deléham, Aug 23 2007

EXTENSIONS

More terms from Olivier Gérard, Sep 22 2007

STATUS

approved

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Last modified February 22 11:30 EST 2018. Contains 299452 sequences. (Running on oeis4.)