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%I #36 Jul 12 2023 12:54:31
%S 1,50,2500,125000,6250000,312500000,15625000000,781250000000,
%T 39062500000000,1953125000000000,97656250000000000,
%U 4882812500000000000,244140625000000000000,12207031250000000000000,610351562500000000000000
%N Powers of 50.
%C 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.
%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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