Search: id:A000420
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%I A000420 M4431 N1874
%S A000420 1,7,49,343,2401,16807,117649,823543,5764801,40353607,282475249,1977326743,
%T A000420 13841287201,96889010407,678223072849,4747561509943,33232930569601,232630513987207,
%U A000420 1628413597910449,11398895185373143,79792266297612001,558545864083284007
%N A000420 Powers of 7.
%C A000420 Same as Pisot sequences E(1,7), L(1,7), P(1,7), T(1,7). See A008776 for 
               definitions of Pisot sequences.
%C A000420 With a different offset, number of n-permutations (n>=0) of 8 objects: 
               s, 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 15 2008
%D A000420 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000420 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000420 T. D. Noe, <a href="b000420.txt">Table of n, a(n) for n=0..100</a>
%H A000420 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 A000420 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=272">
               Encyclopedia of Combinatorial Structures 272</a>
%H A000420 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A000420 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 A000420 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 A000420 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 A000420 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A000420 a(n) = 7^n; a(n) = 7a(n-1).
%F A000420 G.f.: 1/(1-7x), e.g.f.: exp(7x)
%p A000420 A000420:=-1/(-1+7*z); [Conjectured by S. Plouffe in his 1992 dissertation.]
%p A000420 with(finance):seq(futurevalue(1,6,n), n=0..21);# [From Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Mar 25 2009]
%o A000420 (Other) sage: [lucas_number1(n,7,0) for n in xrange(1, 23)]# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
%Y A000420 Sequence in context: A124536 A045578 A126627 this_sequence A050737 A033143 
               A024582
%Y A000420 Adjacent sequences: A000417 A000418 A000419 this_sequence A000421 A000422 
               A000423
%K A000420 nonn,easy
%O A000420 0,2
%A A000420 N. J. A. Sloane (njas(AT)research.att.com).

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