A067419 Fourth column of triangle A067417.

1, 6, 72, 864, 10368, 124416, 1492992, 17915904, 214990848, 2579890176, 30958682112, 371504185344, 4458050224128, 53496602689536, 641959232274432, 7703510787293184, 92442129447518208, 1109305553370218496, 13311666640442621952, 159739999685311463424

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Index entries for linear recurrences with constant coefficients, signature (12).

Formula

a(n) = A067417(n+3,3).

a(n) = 6*(3*4)^(n-1), n >= 1, a(0)=1.

G.f.: (1-6*x)/(1-12*x).

a(n) = Sum_{k=0..n} A134309(n,k)*6^k = Sum_{k=0..n} A055372(n,k)*5^k. - Philippe Deléham, Feb 04 2012

From Elmo R. Oliveira, Jun 07 2026: (Start)

a(n) = 12*a(n-1) for n > 1.

E.g.f.: (1 + exp(12*x))/2 = exp(6*x)*cosh(6*x). (End)

Mathematica

Join[{1}, NestList[12*# &, 6, 20]] (* Paolo Xausa, Sep 03 2024 *)

Prog

(Magma) [Ceiling(6*(3*4)^(n-1)): n in [0..20]]; // Vincenzo Librandi, Oct 02 2011

Crossrefs

Cf. A055372, A067417, A134309.

Cf. A067403 (third column), A067420 (fifth column), A001021 (powers of 12).

Sequence in context: A105928 A186665 A007031 * A113331 A333593 A389175

Adjacent sequences: A067416 A067417 A067418 * A067420 A067421 A067422

Keyword

nonn,easy

Author

Wolfdieter Lang, Jan 25 2002

Status

approved