A009970 Powers of 26.

1, 26, 676, 17576, 456976, 11881376, 308915776, 8031810176, 208827064576, 5429503678976, 141167095653376, 3670344486987776, 95428956661682176, 2481152873203736576, 64509974703297150976, 1677259342285725925376, 43608742899428874059776, 1133827315385150725554176, 29479510200013918864408576, 766467265200361890474622976, 19928148895209409152340197376

Offset

0,2

Comments

Same as Pisot sequences E(1, 26), L(1, 26), P(1, 26), T(1, 26). Essentially same as Pisot sequences E(26, 676), L(26, 676), P(26, 676), T(26, 676). 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 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 range(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: A360509 A188697 A188696 * A041313 A042302 A097835

Adjacent sequences: A009967 A009968 A009969 * A009971 A009972 A009973

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved