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A009969 Powers of 25. 26
1, 25, 625, 15625, 390625, 9765625, 244140625, 6103515625, 152587890625, 3814697265625, 95367431640625, 2384185791015625, 59604644775390625, 1490116119384765625, 37252902984619140625, 931322574615478515625, 23283064365386962890625, 582076609134674072265625, 14551915228366851806640625, 363797880709171295166015625, 9094947017729282379150390625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A000005(a(n)) = A005408(n+1). - Reinhard Zumkeller, Mar 04 2007

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 25-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

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 (25).

FORMULA

G.f.: 1/(1-25*x). - Philippe Deléham, Nov 23 2008

E.g.f.: exp(25*x) - Zerinvary Lajos, Apr 29 2009

a(n)=25^n; a(n)=25*a(n-1) n>0 a(0)=1 [From Vincenzo Librandi, Nov 21 2010]

MATHEMATICA

25^Range[0, 20] (* or *) NestList[25#&, 1, 20] (* Harvey P. Dale, Dec 12 2016 *)

PROG

(Sage) [lucas_number1(n, 25, 0) for n in xrange(1, 17)]# - Zerinvary Lajos, Apr 29 2009

(MAGMA)[25^n: n in [0..100]] [From Vincenzo Librandi, Nov 21 2010]

(PARI) a(n)=25^n \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Sequence in context: A207196 A207216 A171299 * A042202 A203341 A260048

Adjacent sequences:  A009966 A009967 A009968 * A009970 A009971 A009972

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified April 28 05:37 EDT 2017. Contains 285557 sequences.