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A009973 Powers of 29. 36
1, 29, 841, 24389, 707281, 20511149, 594823321, 17249876309, 500246412961, 14507145975869, 420707233300201, 12200509765705829, 353814783205469041, 10260628712958602189, 297558232675799463481, 8629188747598184440949 (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 29-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

Numbers n such that sigma(29*n) = 29*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 (29).

FORMULA

G.f.: 1/(1-29*x). - Philippe Deléham, Nov 24 2008

a(n) = 29^n; a(n) = 29*a(n-1) for n>0, a(0)=1. - Vincenzo Librandi, Nov 21 2010

G.f.: (G(0)-2)/(9*x), where G(k)= 1 + 1/(1 - x*(9*k-9)/(x*(9*k+20) - 2/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 17 2013

MAPLE

A009973:=n->29^n; seq(A009973(n), n=0..20); # Wesley Ivan Hurt, Jun 06 2014

MATHEMATICA

29^Range[0, 20] (* Harvey P. Dale, Jul 19 2011 *)

PROG

(Sage) [29^n for n in (1..17)] # Zerinvary Lajos, Apr 29 2009

(MAGMA) [29^n: n in [0..30]]; // Vincenzo Librandi, Nov 21 2010

(Maxima) makelist(29^n, n, 0, 30); /* Martin Ettl, Nov 07 2012 */

(PARI) a(n)=29^n \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Sequence in context: A223679 A171303 A262337 * A278475 A057687 A049667

Adjacent sequences:  A009970 A009971 A009972 * A009974 A009975 A009976

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 11 1996

STATUS

approved

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Last modified May 28 00:50 EDT 2017. Contains 287210 sequences.