A069996 Number of spanning trees on the bipartite graph K_{3,n}.

1, 12, 81, 432, 2025, 8748, 35721, 139968, 531441, 1968300, 7144929, 25509168, 89813529, 312487308, 1076168025, 3673320192, 12440502369, 41841412812, 139858796529, 464904586800, 1537671920841, 5062810950252, 16600580533161

Offset

1,2

Comments

With a leading zero, this is the second binomial transform of the octagonal numbers A000567 and the binomial transform of A084857. - Paul Barry, Jun 09 2003

Links

Table of n, a(n) for n=1..23.

Index entries for linear recurrences with constant coefficients, signature (9,-27,27).

Formula

a(n) = n^2 * 3^(n-1).

E.g.f.: exp(3x)(x+3x^2). - Paul Barry, Jul 23 2003

a(n) = 9*a(n-1)-27*a(n-2)+27*a(n-3). G.f.: x*(1+3*x)/(1-3*x)^3. - Colin Barker, Aug 10 2012

G.f.: 1 + 12*x/(G(0) - 12*x), where G(k)= 1 + 12*x + 2*k*(6*x+1) + (1+3*x)*k^2 - 3*x*(k+1)^2*(k+3)^2/G(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Jul 05 2013

Mathematica

a[n_] := n^2*3^(n - 1); Table[ a[n], {n, 1, 24}]

Crossrefs

Cf. A000567, A084857.

Sequence in context: A012195 A147650 A007010 * A183504 A194493 A163020

Adjacent sequences: A069993 A069994 A069995 * A069997 A069998 A069999

Keyword

nonn,easy

Author

Eric Weinhandl (eweinhandl(AT)msn.com), May 01 2002

Extensions

Edited and extended by Robert G. Wilson v, May 04 2002

Status

approved