0,2

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

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).

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)

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

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

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

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

Sequence in context: A208368 A207716 A208077 * A041841 A236270 A382874

Adjacent sequences: A009983 A009984 A009985 * A009987 A009988 A009989

nonn,easy

approved