A226511 a(n) = 3*(5^n-3^n)/2.

0, 3, 24, 147, 816, 4323, 22344, 113907, 576096, 2900163, 14559864, 72976467, 365413776, 1828663203, 9148098984, 45754843827, 228817265856, 1144215469443, 5721464767704, 28608486099987, 143045917284336, 715240046774883, 3576231614934024, 17881252217848947, 89406543518781216

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Max A. Alekseyev and T. Berger, Solving the Tower of Hanoi with Random Moves. In: J. Beineke, J. Rosenhouse (eds.) The Mathematics of Various Entertaining Subjects: Research in Recreational Math, Princeton University Press, 2016, pp. 65-79. ISBN 978-0-691-16403-8

Index entries for linear recurrences with constant coefficients, signature (8,-15).

Formula

G.f.: 3*x/((1-5*x)*(1-3*x)). - Vincenzo Librandi, Jun 12 2013

a(n) = 8*a(n-1) -15*a(n-2) for n>1, a(0)=0, a(1)=3. - Vincenzo Librandi, Jun 12 2013

a(n) = A005059(n)*3 = A005058(n)*3/2.

Mathematica

CoefficientList[Series[3 x / ((1 - 5 x) (1 - 3 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 12 2013 *)
Table[3 (5^n - 3^n)/2, {n, 0, 25}] (* Bruno Berselli, Jun 12 2013 *)

Prog

(Magma) [(3/2)*(5^n-3^n): n in [0..30]]; // Vincenzo Librandi, Jun 12 2013

Crossrefs

Cf. A005058.

Sequence in context: A056344 A201231 A212698 * A125651 A043017 A003443

Adjacent sequences: A226508 A226509 A226510 * A226512 A226513 A226514

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 12 2013

Status

approved