cp's OEIS Frontend

A009969 Powers of 25.

%I A009969 #50 Jul 12 2023 12:35:03
%S A009969 1,25,625,15625,390625,9765625,244140625,6103515625,152587890625,
%T A009969 3814697265625,95367431640625,2384185791015625,59604644775390625,
%U A009969 1490116119384765625,37252902984619140625,931322574615478515625,23283064365386962890625,582076609134674072265625,14551915228366851806640625,363797880709171295166015625,9094947017729282379150390625
%N A009969 Powers of 25.
%C A009969 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 A009969 A000005(a(n)) = A005408(n+1). - _Reinhard Zumkeller_, Mar 04 2007
%C A009969 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 A009969 T. D. Noe, <a href="/A009969/b009969.txt">Table of n, a(n) for n = 0..100</a>
%H A009969 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A009969 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (25).
%F A009969 G.f.: 1/(1-25*x). - _Philippe Deléham_, Nov 23 2008
%F A009969 E.g.f.: exp(25*x). - _Zerinvary Lajos_, Apr 29 2009
%F A009969 a(n) = 25^n; a(n) = 25*a(n-1), n > 0; a(0)=1. - _Vincenzo Librandi_, Nov 21 2010
%F A009969 a(n) = A000351(2n) = 5^(2n). - _M. F. Hasler_, Sep 02 2021
%t A009969 25^Range[0,20] (* or *) NestList[25#&,1,20] (* _Harvey P. Dale_, Dec 12 2016 *)
%o A009969 (Sage) [lucas_number1(n,25,0) for n in range(1, 17)] # _Zerinvary Lajos_, Apr 29 2009
%o A009969 (Magma) [25^n: n in [0..100]] // _Vincenzo Librandi_, Nov 21 2010
%o A009969 (PARI) a(n)=25^n \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A009969 Bisection of A000351 (powers of 5).
%Y A009969 Cf. A218728 (partial sums).
%K A009969 nonn,easy
%O A009969 0,2
%A A009969 _N. J. A. Sloane_