A009969 Powers of 25.

1, 25, 625, 15625, 390625, 9765625, 244140625, 6103515625, 152587890625, 3814697265625, 95367431640625, 2384185791015625, 59604644775390625, 1490116119384765625, 37252902984619140625, 931322574615478515625, 23283064365386962890625, 582076609134674072265625, 14551915228366851806640625, 363797880709171295166015625, 9094947017729282379150390625

Offset

0,2

Comments

Same as Pisot sequences E(1, 25), L(1, 25), P(1, 25), T(1, 25). Essentially same as Pisot sequences E(25, 625), L(25, 625), P(25, 625), T(25, 625). See A008776 for definitions of Pisot sequences.

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. - Vincenzo Librandi, Nov 21 2010

a(n) = A000351(2n) = 5^(2n). - M. F. Hasler, Sep 02 2021

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 range(1, 17)] # Zerinvary Lajos, Apr 29 2009
(Magma) [25^n: n in [0..100]] // Vincenzo Librandi, Nov 21 2010
(PARI) a(n)=25^n \\ Charles R Greathouse IV, Sep 24 2015

Crossrefs

Bisection of A000351 (powers of 5).

Cf. A218728 (partial sums).

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