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A009970 Powers of 26. 4
1, 26, 676, 17576, 456976, 11881376, 308915776, 8031810176, 208827064576, 5429503678976, 141167095653376, 3670344486987776, 95428956661682176, 2481152873203736576, 64509974703297150976, 1677259342285725925376, 43608742899428874059776, 1133827315385150725554176, 29479510200013918864408576, 766467265200361890474622976, 19928148895209409152340197376 (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 26-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

Number of n-letter words over an alphabet with 26 letters. - Wesley Ivan Hurt, Apr 17 2016

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 (26).

FORMULA

G.f.: 1/(1-26*x). - Philippe Deléham, Nov 23 2008

E.g.f.: exp(26*x). - Zerinvary Lajos, Apr 29 2009

From Vincenzo Librandi, Nov 21 2010: (Start)

a(n) = 26*a(n-1) for n > 0, a(0) = 1.

a(n) = 26^n. (End)

MAPLE

A009970:=n->26^n: seq(A009970(n), n=0..25); # Wesley Ivan Hurt, Apr 17 2016

MATHEMATICA

26^Range[0, 25] (* Alonso del Arte, Mar 25 2015 *)

NestList[26#&, 1, 20] (* Harvey P. Dale, Jan 14 2017 *)

PROG

(Sage) [lucas_number1(n, 26, 0) for n in xrange(1, 17)] # Zerinvary Lajos, Apr 29 2009

(MAGMA)[26^n: n in [0..100]] // Vincenzo Librandi, Nov 21 2010

(Maxima) A009970(n):=26^n$

makelist(A009970(n), n, 0, 30); /* Martin Ettl, Nov 07 2012 */

CROSSREFS

Sequence in context: A171300 A188697 A188696 * A041313 A042302 A031423

Adjacent sequences:  A009967 A009968 A009969 * A009971 A009972 A009973

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 20 16:53 EDT 2017. Contains 289628 sequences.