A130977 G.f.: 5/(2 + 3*sqrt(1-20*x)).

1, 6, 66, 876, 12786, 197796, 3183156, 52718616, 892401426, 15368638836, 268388185596, 4741271556456, 84573471344916, 1521119577791976, 27554494253636136, 502257203287150896, 9205363627419463506

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

Column k=6 of A183135.

Sequence in context: A004355 A282046 A124862 * A191096 A151832 A378840

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