A009987 Powers of 43.

1, 43, 1849, 79507, 3418801, 147008443, 6321363049, 271818611107, 11688200277601, 502592611936843, 21611482313284249, 929293739471222707, 39959630797262576401, 1718264124282290785243, 73885357344138503765449

Offset

0,2

Comments

Same as Pisot sequences E(1, 43), L(1, 43), P(1, 43), T(1, 43). Essentially same as Pisot sequences E(43, 1849), L(43, 1849), P(43, 1849), T(43, 1849). 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 43-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

Numbers n such that sigma(43*n) = 43*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 (43).

Formula

G.f.: 1/(1-43*x). - Philippe Deléham, Nov 24 2008

a(n) = 43^n; a(n) = 43*a(n-1), a(0)=1. - Vincenzo Librandi, Nov 21 2010

Mathematica

43^Range[0, 20] (* Harvey P. Dale, Nov 30 2014 *)

Prog

(Magma)[43^n: n in [0..20]] // Vincenzo Librandi, Nov 21 2010
(PARI) a(n)=43^n \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Sequence in context: A218745 A331777 A262470 * A267532 A335207 A076572

Adjacent sequences: A009984 A009985 A009986 * A009988 A009989 A009990

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved