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A193132
a(n) = 3n*4^(2n-1).
2
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
Eric Weisstein's World of Mathematics, Crossed Prism Graph.
Eric Weisstein's World of Mathematics, Spanning Tree.
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jul 16 2011
STATUS
approved