A009991 Powers of 47.

1, 47, 2209, 103823, 4879681, 229345007, 10779215329, 506623120463, 23811286661761, 1119130473102767, 52599132235830049, 2472159215084012303, 116191483108948578241, 5460999706120583177327

Offset

0,2

Comments

Same as Pisot sequences E(1, 47), L(1, 47), P(1, 47), T(1, 47). Essentially same as Pisot sequences E(47, 2209), L(47, 2209), P(47, 2209), T(47, 2209). 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 47-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

Numbers n such that sigma(47*n) = 47*n + sigma(n). - Jahangeer Kholdi, Nov 24 2013

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 (47).

Formula

G.f.: 1/(1-47*x). - Philippe Deléham, Nov 24 2008

a(n) = 47^n; a(n) = 47*a(n-1), a(0)=1. - Vincenzo Librandi, Nov 21 2010

Mathematica

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

Prog

(Magma)[47^n: n in [0..20]] // Vincenzo Librandi, Nov 21 2010
(PARI) a(n)=47^n \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Sequence in context: A170766 A218749 A049668 * A374306 A052463 A327770

Adjacent sequences: A009988 A009989 A009990 * A009992 A009993 A009994

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved