A009985 Powers of 41.

1, 41, 1681, 68921, 2825761, 115856201, 4750104241, 194754273881, 7984925229121, 327381934393961, 13422659310152401, 550329031716248441, 22563490300366186081, 925103102315013629321, 37929227194915558802161

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Same as Pisot sequences E(1, 41), L(1, 41), P(1, 41), T(1, 41). Essentially same as Pisot sequences E(41, 1681), L(41, 1681), P(41, 1681), T(41, 1681). 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 41-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

Numbers n such that sigma(41*n) = 41*n + sigma(n). - Jahangeer Kholdi, Nov 23 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 (41).

Programs

Magma

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

Mathematica

41^Range[0, 14] (* Alonso del Arte, Sep 04 2015 *)
NestList[41#&,1,20] (* Harvey P. Dale, Mar 07 2017 *)

PARI

first(m)=vector(m,i,i--;41^i) \\ Anders Hellström, Sep 12 2015

Formula

G.f.: 1/(1-41*x). - Philippe Deléham, Nov 24 2008

a(n) = 41^n; a(n) = 41*a(n-1), a(0)=1. - Vincenzo Librandi, Nov 21 2010