A165800 Powers of 50.

1, 50, 2500, 125000, 6250000, 312500000, 15625000000, 781250000000, 39062500000000, 1953125000000000, 97656250000000000, 4882812500000000000, 244140625000000000000, 12207031250000000000000, 610351562500000000000000, 30517578125000000000000000, 1525878906250000000000000000

Offset: 0

Author

Jaroslav Krizek, Sep 27 2009

Keywords

• nonn
• easy

Comments

Same as Pisot sequences E(1, 50), L(1, 50), P(1, 50), T(1, 50). Essentially same as Pisot sequences E(50, 2500), L(50, 2500), P(50, 2500), T(50, 2500). 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 50-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
• Index entries for linear recurrences with constant coefficients, signature (50).

Crossrefs

Cf. A000079, A000351, A008776, A011557, A098608.

Programs

Magma

[50^n: n in [0..20]]; // Vincenzo Librandi, Nov 21 2010

Mathematica

50^Range[0, 20] (* Paolo Xausa, Jul 09 2025 *)

Maxima

A165800(n):=50^n$
makelist(A165800(n),n,0,30); /* Martin Ettl, Nov 06 2012 */

PARI

a(n)=50^n \\ Charles R Greathouse IV, Jun 19 2015

PARI

powers(50,8) \\ Charles R Greathouse IV, Jun 19 2015

Formula

G.f.: 1/(1-50*x).

a(n) = 50^n; a(n) = 50*a(n-1) a(0)=1. - Vincenzo Librandi, Nov 21 2010

From G. C. Greubel, Apr 08 2016: (Start)

a(n) = 2^n * 5^(2*n) = A000079(n)*A000351(n)^2.

a(n) = 5^n * 10^n = A000351(n)*A011557(n). (End)

From Elmo R. Oliveira, Jul 08 2025: (Start)

E.g.f.: exp(50*x).

a(n) = A098608(n)/A000079(n). (End)