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A165800 Powers of 50. 5
1, 50, 2500, 125000, 6250000, 312500000, 15625000000, 781250000000, 39062500000000, 1953125000000000, 97656250000000000, 4882812500000000000, 244140625000000000000, 12207031250000000000000, 610351562500000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = 50^n.

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

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Last modified May 26 21:58 EDT 2018. Contains 304645 sequences. (Running on oeis4.)