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

Author

Wolfdieter Lang, Jan 25 2002

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..900
• Index entries for linear recurrences with constant coefficients, signature (12).

Crossrefs

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

Programs

Magma

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

Mathematica

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

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