A009987 Powers of 43.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Programs

Magma

[43^n: n in [0..20]]; // Vincenzo Librandi, Nov 21 2010

Mathematica

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

PARI

a(n)=43^n \\ Charles R Greathouse IV, Oct 07 2015

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