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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Programs

Magma

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

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 *)

Maxima

A009970(n):=26^n$
makelist(A009970(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

Sage

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

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)