A165800 Powers of 50.

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

Offset

0,2

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).

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

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

Prog

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

Crossrefs

Cf. A000079, A000351, A011557.

Sequence in context: A223845 A223871 A223796 * A042201 A097838 A203842

Adjacent sequences: A165797 A165798 A165799 * A165801 A165802 A165803

Keyword

nonn,easy

Author

Jaroslav Krizek, Sep 27 2009

Status

approved