A009990 Powers of 46.

1, 46, 2116, 97336, 4477456, 205962976, 9474296896, 435817657216, 20047612231936, 922190162669056, 42420747482776576, 1951354384207722496, 89762301673555234816, 4129065876983540801536, 189937030341242876870656, 8737103395697172336050176, 401906756202069927458308096

Offset

0,2

Comments

Same as Pisot sequences E(1, 46), L(1, 46), P(1, 46), T(1, 46). Essentially same as Pisot sequences E(46, 2116), L(46, 2116), P(46, 2116), T(46, 2116). 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 46-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 (46).

Formula

G.f.: 1/(1-46*x). - Philippe Deléham, Nov 24 2008

a(n) = 46^n; a(n) = 46*a(n-1), a(0)=1. - Vincenzo Librandi, Nov 21 2010

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

E.g.f.: exp(46*x).

a(n) = A000079(n)*A009967(n). (End)

Mathematica

46^Range[0, 20] (* or *) NestList[46#&, 1, 20] (* Harvey P. Dale, Jan 15 2017 *)

Prog

(Magma)[46^n: n in [0..20]]; // Vincenzo Librandi, Nov 21 2010

Crossrefs

Cf. A000079, A008776, A009967.

Sequence in context: A223785 A264525 A223971 * A042013 A333718 A234153

Adjacent sequences: A009987 A009988 A009989 * A009991 A009992 A009993

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved