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A009985 Powers of 41. 7
1, 41, 1681, 68921, 2825761, 115856201, 4750104241, 194754273881, 7984925229121, 327381934393961, 13422659310152401, 550329031716248441, 22563490300366186081, 925103102315013629321, 37929227194915558802161 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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).

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

MATHEMATICA

41^Range[0, 14] (* Alonso del Arte, Sep 04 2015 *)

NestList[41#&, 1, 20] (* Harvey P. Dale, Mar 07 2017 *)

PROG

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

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

CROSSREFS

Sequence in context: A170722 A170760 A218743 * A147521 A233070 A267267

Adjacent sequences:  A009982 A009983 A009984 * A009986 A009987 A009988

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 23 00:16 EDT 2017. Contains 290953 sequences.