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 A165800 Powers of 50. 5

%I

%S 1,50,2500,125000,6250000,312500000,15625000000,781250000000,

%T 39062500000000,1953125000000000,97656250000000000,

%U 4882812500000000000,244140625000000000000,12207031250000000000000,610351562500000000000000

%N Powers of 50.

%C a(n) = 50^n.

%C 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

%H T. D. Noe, <a href="/A165800/b165800.txt">Table of n, a(n) for n = 0..100</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (50).

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

%F a(n) = 50^n; a(n) = 50*a(n-1) a(0)=1. - _Vincenzo Librandi_, Nov 21 2010

%F From _G. C. Greubel_, Apr 08 2016: (Start)

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

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

%o (MAGMA) [50^n: n in [0..20]] // _Vincenzo Librandi_, Nov 21 2010

%o (Maxima) A165800(n):=50^n\$

%o makelist(A165800(n),n,0,30); /* _Martin Ettl_, Nov 06 2012 */

%o (PARI) a(n)=50^n \\ _Charles R Greathouse IV_, Jun 19 2015

%o (PARI) powers(50,8) \\ _Charles R Greathouse IV_, Jun 19 2015

%Y Cf. A000079, A000351, A011557.

%K nonn,easy

%O 0,2

%A _Jaroslav Krizek_, Sep 27 2009

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Last modified December 12 07:00 EST 2019. Contains 329948 sequences. (Running on oeis4.)