A193132 a(n) = 3n*4^(2n-1).

12, 384, 9216, 196608, 3932160, 75497472, 1409286144, 25769803776, 463856467968, 8246337208320, 145135534866432, 2533274790395904, 43910096366862336, 756604737398243328, 12970366926827028480, 221360928884514619392, 3763135791036748529664

Offset: 1

Author

Eric W. Weisstein, Jul 16 2011

Keywords

• nonn
• easy

Comments

a(n) is the number of spanning trees for the 2n-crossed prism graph with n >= 2.

Sequence extended to n=1 using the closed form.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..300
• Eric Weisstein's World of Mathematics, Crossed Prism Graph.
• Eric Weisstein's World of Mathematics, Spanning Tree.
• Index entries for sequences related to trees.
• Index entries for linear recurrences with constant coefficients, signature (32,-256).

Crossrefs

Cf. A267796.

Programs

Magma

[3*n*4^(2*n-1): n in [1..20]]; // Vincenzo Librandi, Jul 17 2011

Mathematica

LinearRecurrence[{32,-256},{12,384},20] (* Harvey P. Dale, Apr 08 2015 *)

PARI

a(n)=3*n<<(4*n-2) \\ Charles R Greathouse IV, Jul 30 2011

Formula

O.g.f.: 12*x/(16*x-1)^2.

a(n) = 32*a(n-1) - 256*a(n-2). - Harvey P. Dale, Apr 08 2015

From Amiram Eldar, Apr 17 2022: (Start)

a(n) = 3*A267796(n-1).

Sum_{n>=1} 1/a(n) = (4/3)*log(16/15).

Sum_{n>=1} (-1)^(n+1)/a(n) = (4/3)*log(17/16). (End)