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A009967

Powers of 23.

1, 23, 529, 12167, 279841, 6436343, 148035889, 3404825447, 78310985281, 1801152661463, 41426511213649, 952809757913927, 21914624432020321, 504036361936467383, 11592836324538749809, 266635235464391245607, 6132610415680998648961, 141050039560662968926103, 3244150909895248285300369, 74615470927590710561908487, 1716155831334586342923895201

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

Same as Pisot sequences E(1, 23), L(1, 23), P(1, 23), T(1, 23). Essentially same as Pisot sequences E(23, 529), L(23, 529), P(23, 529), T(23, 529). 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 23-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

Numbers k such that sigma(23*k) = 23*k + sigma(k). - 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 (23).

FORMULA

G.f.: 1/(1-23*x). - Philippe Deléham, Nov 23 2008

a(n) = 23^n; a(n) = 23*a(n-1) n>0 a(0)=1. - Vincenzo Librandi, Nov 21 2010

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

E.g.f.: exp(23*x).

a(n) = A009990(n)/A000079(n). (End)

MATHEMATICA