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

1,1

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).

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)

Mathematica

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

Prog

(Magma) [3*n*4^(2*n-1): n in [1..20]]; // Vincenzo Librandi, Jul 17 2011
(PARI) a(n)=3*n<<(4*n-2) \\ Charles R Greathouse IV, Jul 30 2011

Crossrefs

Cf. A267796.

Sequence in context: A251590 A352651 A196459 * A326214 A187513 A138914

Adjacent sequences: A193129 A193130 A193131 * A193133 A193134 A193135

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 16 2011

Status

approved