A009986 Powers of 42.

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

Offset

0,2

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).

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

Mathematica

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

Prog

(Magma)[42^n: n in [0..20]] // Vincenzo Librandi, Nov 21 2010
(PARI) a(n) = 42^n; \\ Michel Marcus, Jan 14 2018

Crossrefs

Sequence in context: A208368 A207716 A208077 * A041841 A236270 A216703

Adjacent sequences: A009983 A009984 A009985 * A009987 A009988 A009989

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved