A009982 Powers of 38.

1, 38, 1444, 54872, 2085136, 79235168, 3010936384, 114415582592, 4347792138496, 165216101262848, 6278211847988224, 238572050223552512, 9065737908494995456, 344498040522809827328, 13090925539866773438464, 497455170514937390661632, 18903296479567620845142016

Offset

0,2

Comments

Same as Pisot sequences E(1, 38), L(1, 38), P(1, 38), T(1, 38). Essentially same as Pisot sequences E(38, 1444), L(38, 1444), P(38, 1444), T(38, 1444). 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 38-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011. [See A000244 for a proof.]

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 (38).

Formula

G.f.: 1/(1 - 38*x). - Philippe Deléham, Nov 24 2008

a(n) = 38^n; a(n) = 38*a(n-1), n > 0, a(0) = 1. - Vincenzo Librandi, Nov 21 2010

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

E.g.f.: exp(38*x).

a(n) = A000079(n)*A001029(n). (End)

Mathematica

38^Range[0, 19] (* Alonso del Arte, Feb 18 2017 *)

Prog

(Magma) [38^n: n in [0..20]]; // Vincenzo Librandi, Nov 21 2010
(PARI) a(n)=38^n \\ M. F. Hasler, Feb 21 2017

Crossrefs

Cf. A000079, A000244, A001029, A008776.

Sequence in context: A158702 A239364 A078987 * A041685 A221385 A158766

Adjacent sequences: A009979 A009980 A009981 * A009983 A009984 A009985

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved