Search: id:A001018
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%I A001018 M4555 N1937
%S A001018 1,8,64,512,4096,32768,262144,2097152,16777216,134217728,1073741824,
%T A001018 8589934592,68719476736,549755813888,4398046511104,35184372088832,281474976710656,
%U A001018 2251799813685248,18014398509481984,144115188075855872,1152921504606846976,
               9223372036854775808,73786976294838206464,590295810358705651712
%N A001018 Powers of 8.
%C A001018 Same as Pisot sequences E(1,8), L(1,8), P(1,8), T(1,8). See A008776 for 
               definitions of Pisot sequences.
%C A001018 If X_1, X_2, ..., X_n is a partition of the set {1,2,...,2*n} into blocks 
               of size 2 then, for n>=1, a(n) is equal to the number of functions 
               f : {1,2,..., 2*n}->{1,2,3} such that for fixed y_1,y_2,...,y_n in 
               {1,2,3} we have f(X_i)<>{y_i}, (i=1,2,...,n). - Milan R. Janjic (agnus(AT)blic.net), 
               May 24 2007
%C A001018 With a different offset, number of n-permutations (n>=0) of 9 objects: 
               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 15 2008
%C A001018 1/1 + 1/8 + 1/64 + 1/512 + 1/4096 + ... = 8/7 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Aug 29 2008]
%C A001018 a(n) = A157176(A008588(n)); a(n+1) = A157176(A016969(n)). [From Reinhard 
               Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 24 2009]
%C A001018 This is the auto-convolution (convolution square) of A059304. [From R. 
               J. Mathar (mathar(AT)strw.leidenuniv.nl), May 25 2009]
%D A001018 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001018 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A001018 T. D. Noe, <a href="b001018.txt">Table of n, a(n) for n=0..100</a>
%H A001018 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 A001018 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=273">
               Encyclopedia of Combinatorial Structures 273</a>
%H A001018 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas 
               for Some Functions on Finite Sets</a>
%H A001018 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A001018 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 A001018 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SierpinskiCarpet.html">Sierpinski Carpet</a>
%H A001018 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A001018 a(n) = 8^n; a(n) = 8a(n-1).
%F A001018 G.f.: 1/(1-8x), e.g.f.: exp(8x)
%p A001018 with(finance):seq(futurevalue(1,7,n), n=0..20);# [From Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Mar 25 2009]
%o A001018 (Other) sage: [lucas_number1(n,8,0) for n in xrange(1, 22)]# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
%Y A001018 A013730, A103333, A013731, A067417, A083233, A055274. [From Reinhard 
               Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 24 2009]
%Y A001018 Sequence in context: A126629 A125498 A125908 this_sequence A097682 A050738 
               A046238
%Y A001018 Adjacent sequences: A001015 A001016 A001017 this_sequence A001019 A001020 
               A001021
%K A001018 nonn,easy
%O A001018 0,2
%A A001018 N. J. A. Sloane (njas(AT)research.att.com).
%E A001018 More terms a(21), a(22), a(23) from Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Aug 06 2009

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