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%I #50 Jul 12 2023 12:35:03
%S 1,25,625,15625,390625,9765625,244140625,6103515625,152587890625,
%T 3814697265625,95367431640625,2384185791015625,59604644775390625,
%U 1490116119384765625,37252902984619140625,931322574615478515625,23283064365386962890625,582076609134674072265625,14551915228366851806640625,363797880709171295166015625,9094947017729282379150390625
%N Powers of 25.
%C Same as Pisot sequences E(1, 25), L(1, 25), P(1, 25), T(1, 25). Essentially same as Pisot sequences E(25, 625), L(25, 625), P(25, 625), T(25, 625). See A008776 for definitions of Pisot sequences.
%C A000005(a(n)) = A005408(n+1). - _Reinhard Zumkeller_, Mar 04 2007
%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 25-colored compositions of n such that no adjacent parts have the same color. - _Milan Janjic_, Nov 17 2011
%H T. D. Noe, <a href="/A009969/b009969.txt">Table of n, a(n) for n = 0..100</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (25).
%F G.f.: 1/(1-25*x). - _Philippe Deléham_, Nov 23 2008
%F E.g.f.: exp(25*x). - _Zerinvary Lajos_, Apr 29 2009
%F a(n) = 25^n; a(n) = 25*a(n-1), n > 0; a(0)=1. - _Vincenzo Librandi_, Nov 21 2010
%F a(n) = A000351(2n) = 5^(2n). - _M. F. Hasler_, Sep 02 2021
%t 25^Range[0,20] (* or *) NestList[25#&,1,20] (* _Harvey P. Dale_, Dec 12 2016 *)
%o (Sage) [lucas_number1(n,25,0) for n in range(1, 17)] # _Zerinvary Lajos_, Apr 29 2009
%o (Magma) [25^n: n in [0..100]] // _Vincenzo Librandi_, Nov 21 2010
%o (PARI) a(n)=25^n \\ _Charles R Greathouse IV_, Sep 24 2015
%Y Bisection of A000351 (powers of 5).
%Y Cf. A218728 (partial sums).
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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