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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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified September 27 14:36 EDT 2022. Contains 357062 sequences. (Running on oeis4.)