A009986 Powers of 42.

1, 42, 1764, 74088, 3111696, 130691232, 5489031744, 230539333248, 9682651996416, 406671383849472, 17080198121677824, 717368321110468608, 30129469486639681536, 1265437718438866624512, 53148384174432398229504, 2232232135326160725639168, 93753749683698750476845056

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Same as Pisot sequences E(1, 42), L(1, 42), P(1, 42), T(1, 42). Essentially same as Pisot sequences E(42, 1764), L(42, 1764), P(42, 1764), T(42, 1764). See A008776 for definitions of Pisot sequences.

The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n >= 1, a(n) equals the number of 42-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

Links

• T. D. Noe, Table of n, a(n) for n = 0..100
• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (42).

Crossrefs

Cf. A000079, A000400, A000420, A008776, A009965.

Programs

Magma

[42^n: n in [0..20]]; // Vincenzo Librandi, Nov 21 2010

Mathematica

42^Range[0, 14] (* Michael De Vlieger, Jan 13 2018 *)

PARI

a(n) = 42^n; \\ Michel Marcus, Jan 14 2018

Formula

G.f.: 1/(1-42*x). - Philippe Deléham, Nov 24 2008

a(n) = 42^n; a(n) = 42*a(n-1), a(0)=1. - Vincenzo Librandi, Nov 21 2010

From Elmo R. Oliveira, Jul 10 2025: (Start)

E.g.f.: exp(42*x).

a(n) = A000079(n)*A009965(n) = A000400(n)*A000420(n). (End)