Search: id:A000400
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%I A000400 M4224 N1765
%S A000400 1,6,36,216,1296,7776,46656,279936,1679616,10077696,60466176,362797056,
%T A000400 2176782336,13060694016,78364164096,470184984576,2821109907456,16926659444736,
%U A000400 101559956668416,609359740010496,3656158440062976,21936950640377856,131621703842267136
%N A000400 Powers of 6.
%C A000400 Same as Pisot sequences E(1,6), L(1,6), P(1,6), T(1,6). See A008776 for 
               definitions of Pisot sequences.
%C A000400 Central terms of the triangle in A036561. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               May 14 2006
%C A000400 A000005(a(n)) = A000290(n+1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Mar 04 2007
%C A000400 With a different offset, number of n-permutations (n>=0) of 7 objects: 
               t, u, v, w, z, x, y with repetition allowed, containing exactly zero 
               (0) or free u's. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jul 16 2008
%D A000400 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000400 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000400 T. D. Noe, <a href="b000400.txt">Table of n, a(n) for n=0..100</a>
%H A000400 C. Banderier and D. Merlini, <a href="http://www.dsi.unifi.it/~merlini/
               poster.ps">Lattice paths with an infinite set of jumps</a>, FPSAC02, 
               Melbourne, 2002.
%H A000400 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 A000400 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=271">
               Encyclopedia of Combinatorial Structures 271</a>
%H A000400 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A000400 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 A000400 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 A000400 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 A000400 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A000400 a(n) = 6^n; a(n) = 6a(n-1).
%F A000400 G.f.: 1/(1-6x), e.g.f.: exp(6x)
%F A000400 ((3+sqrt9)^n-(3-sqrt9)^n)/6. Offset 1. a(3)=36 [From Al Hakanson (hawkuu(AT)gmail.com), 
               Jan 07 2009]
%p A000400 A000400:=-1/(-1+6*z); [Conjectured by S. Plouffe in his 1992 dissertation.]
%p A000400 with(finance):seq(futurevalue(1,5,n), n=0..22);# [From Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Mar 25 2009]
%o A000400 sage: from sage.combinat.sloane_functions import recur_gen2b sage: it 
               =recur_gen2b(1,n/9,n/9,0, lambda n: 0) sage: [it.next() for i in 
               range(23)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 16 
               2008
%o A000400 (Other) sage: [lucas_number1(n,6,0) for n in xrange(1, 24)]# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
%Y A000400 a(n) = A159991(n)/A011577(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               May 02 2009]
%Y A000400 Sequence in context: A007274 A126634 A007275 this_sequence A097681 A050736 
               A033142
%Y A000400 Adjacent sequences: A000397 A000398 A000399 this_sequence A000401 A000402 
               A000403
%K A000400 easy,nonn
%O A000400 0,2
%A A000400 N. J. A. Sloane (njas(AT)research.att.com).

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