%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 pcolored compositions of n. For n>=1, a(n) equals the number of 50colored 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/(150*x).
%F a(n) = 50^n; a(n) = 50*a(n1) 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
