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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Bisection of A000351 (powers of 5).

Cf. A218728 (partial sums).

Programs

Magma

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

Mathematica

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

PARI

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

Sage

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

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