%I A000351 M3937 N1620
%S A000351 1,5,25,125,625,3125,15625,78125,390625,1953125,9765625,48828125,244140625,
%T A000351 1220703125,6103515625,30517578125,152587890625,762939453125,3814697265625,
%U A000351 19073486328125,95367431640625,476837158203125,2384185791015625,11920928955078125
%N A000351 Powers of 5.
%C A000351 Same as Pisot sequences E(1,5), L(1,5), P(1,5), T(1,5). See A008776 for 
               definitions of Pisot sequences.
%C A000351 a(n) has leading digit 1 iff n = A067497 - 1. - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               Jul 09 2002
%C A000351 With interpolated zeros 0,1,0,5,0,25,... (G.f.: x/(1-5x^2)) second inverse 
               binomial transform of Fib(3n)/F(3) (A001076). Binomial transform 
               is A085449. - Paul Barry (pbarry(AT)wit.ie), Mar 14 2004
%C A000351 Sums of rows of the triangles in A013620 and A038220. - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), May 14 2006
%C A000351 With a different offset, number of n-permutations (n>=0) of 6 objects: 
               u, v, w, z, x, y with repetition allowed, containing exactly zero 
               (0) or free u's. For example, n=2, a(2)=25 because we have, vv, vw, 
               vz, vx, vy, wv, ww, wz, wx, wy, zv, zw, zz, zx, zy, xv, xw, xz, xx, 
               xy, yv, yw, yz, yx and yy. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jul 15 2008
%D A000351 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000351 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000351 T. D. Noe, <a href="b000351.txt">Table of n, a(n) for n=0..100</a>
%H A000351 P. J. Cameron, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               Sequences realized by oligomorphic permutation groups</a>, J. Integ. 
               Seqs. Vol. 3 (2000), #00.1.5.
%H A000351 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=270">
               Encyclopedia of Combinatorial Structures 270</a>
%H A000351 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A000351 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A000351 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A000351 Y. Puri and T. Ward, <a href="http://www.cs.uwaterloo.ca/journals/JIS/
               index.html">Arithmetic and growth of periodic orbits</a>, J. Integer 
               Seqs., Vol. 4 (2001), #01.2.1.
%H A000351 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               BoxFractal.html">Box Fractal</a>
%H A000351 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A000351 a(n) = 5^n; a(n) = 5a(n-1).
%F A000351 G.f.: 1/(1-5x), e.g.f.: exp(5x)
%p A000351 [ seq(5^n,n=0..30) ];
%p A000351 A000351:=-1/(-1+5*z); [S. Plouffe in his 1992 dissertation.]
%p A000351 with(finance):seq(futurevalue(1,4,n), n=0..25);# [From Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Mar 25 2009]
%t A000351 Table[5^n, {n, 0, 30}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Apr 06 2006
%o A000351 (Other) sage: [lucas_number1(n,5,0) for n in xrange(1, 25)]# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
%Y A000351 a(n) = A006495(n)^2 + A006496(n)^2.
%Y A000351 a(n) = A159991(n)/A001021(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               May 02 2009]
%Y A000351 Sequence in context: A129066 A102169 A060391 this_sequence A050735 A083590 
               A097680
%Y A000351 Adjacent sequences: A000348 A000349 A000350 this_sequence A000352 A000353 
               A000354
%K A000351 easy,nonn,nice
%O A000351 0,2
%A A000351 N. J. A. Sloane (njas(AT)research.att.com).
%E A000351 Removed attribute "conjectured" from Plouffe g.f R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Mar 11 2009