A009983 Powers of 39.

1, 39, 1521, 59319, 2313441, 90224199, 3518743761, 137231006679, 5352009260481, 208728361158759, 8140406085191601, 317475837322472439, 12381557655576425121, 482880748567480579719, 18832349194131742609041

Offset

0,2

Comments

Same as Pisot sequences E(1, 39), L(1, 39), P(1, 39), T(1, 39). Essentially same as Pisot sequences E(39, 1521), L(39, 1521), P(39, 1521), T(39, 1521). 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 39-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 (39).

Formula

G.f.: 1/(1-39*x). - Philippe Deléham, Nov 24 2008

a(n) = 39^n; a(n) = 39*a(n-1), a(0)=1. - Vincenzo Librandi, Nov 21 2010

Mathematica

39^Range[0, 20] (* Harvey P. Dale, Dec 02 2010 *)

Prog

(Magma)[39^n: n in [0..20]] // Vincenzo Librandi, Nov 21 2010
(PARI) a(n)=39^n \\ Charles R Greathouse IV, Nov 18 2011

Crossrefs

Sequence in context: A170758 A218741 A112617 * A269028 A158768 A139191

Adjacent sequences: A009980 A009981 A009982 * A009984 A009985 A009986

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved