Search: id:A001019
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%I A001019 M4653 N1992
%S A001019 1,9,81,729,6561,59049,531441,4782969,43046721,387420489,3486784401,
%T A001019 31381059609,282429536481,2541865828329,22876792454961,205891132094649,
%U A001019 1853020188851841,16677181699666569,150094635296999121,1350851717672992089
%N A001019 Powers of 9.
%C A001019 Same as Pisot sequences E(1,9), L(1,9), P(1,9), T(1,9). See A008776 for 
               definitions of Pisot sequences.
%C A001019 Except for 1, the largest n-th power with n digits. - Amarnath Murthy 
               (amarnath_murthy(AT)yahoo.com), Feb 09 2002
%C A001019 The 2002 comment by Amarnath Murthy should say more precisely "n-th power 
               with *at most* n digits": a(22) has only 21 digits etc., a(44) has 
               only 42 digits etc. [From Hagen von Eitzen (math(AT)von-eitzen.de), 
               May 17 2009]
%C A001019 A000005(a(n)) = A005408(n+1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Mar 04 2007
%C A001019 With a different offset, number of n-permutations (n>=0) of 10 objects: 
               q, r, 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 16 2008
%C A001019 1/1 + 1/9 + 1/81 + ... = 9/8 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Aug 29 2008]
%D A001019 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001019 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A001019 T. D. Noe, <a href="b001019.txt">Table of n, a(n) for n=0..100</a>
%H A001019 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 A001019 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=274">
               Encyclopedia of Combinatorial Structures 274</a>
%H A001019 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A001019 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 A001019 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A001019 a(n) = 9^n; a(n) = 9a(n-1).
%F A001019 G.f.: 1/(1-9x), e.g.f.: exp(9x)
%p A001019 with(finance):seq(futurevalue(1,8,n), n=0..19);# [From Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Mar 25 2009]
%o A001019 sage: from sage.combinat.sloane_functions import recur_gen2b sage: it 
               =recur_gen2b(1,n/6,n/6,0, lambda n: 0) sage: [it.next() for i in 
               range(18)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 16 
               2008
%o A001019 (Other) sage: [lucas_number1(n,9,0) for n in xrange(1, 21)]# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
%Y A001019 Cf. A067470.
%Y A001019 Sequence in context: A120997 A125630 A100062 this_sequence A074118 A050739 
               A158779
%Y A001019 Adjacent sequences: A001016 A001017 A001018 this_sequence A001020 A001021 
               A001022
%K A001019 easy,nonn
%O A001019 0,2
%A A001019 N. J. A. Sloane (njas(AT)research.att.com).

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