%I A004171
%S A004171 2,8,32,128,512,2048,8192,32768,131072,524288,2097152,8388608,33554432,
%T A004171 134217728,536870912,2147483648,8589934592,34359738368,137438953472,549755813888,
%U A004171 2199023255552,8796093022208,35184372088832,140737488355328,562949953421312
%N A004171 2^(2n+1).
%C A004171 Same as Pisot sequences E(2,8), L(2,8), P(2,8), T(2,8). See A008776 for 
               definitions of Pisot sequences.
%C A004171 In the Chebyshev polynomial of degree 2n, a(n) is the coefficient of 
               x^2n. - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 13 2002
%C A004171 1/2 - 1/8 + 1/32 - 1/128 + ... = 2/5 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Mar 03 2009]
%C A004171 Numbers n such that n^3+(n/2)^3=9*n^3/8 is square [From Vincenzo Librandi 
               (vincenzo.librandi(AT)tin.it), Aug 05 2009]
%H A004171 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A004171 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas 
               for Some Functions on Finite Sets</a>
%H A004171 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A004171 a(n) = 2*4^n; a(n) = 4a(n-1).
%F A004171 1 = 1/2 + Sum(n = 1 through infinity) 3/a(n) = 3/6 + 3/8 + 3/32 + 3/128 
               + 3/512 + 3/2048...; with partial sums: 1/2, 31/32, 127/128, 511/
               512, 2047/2048... - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 16 
               2003
%F A004171 a(n)=2*A000302(n) . G.f.: 2/(1-4*x). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 23 2008]
%F A004171 a(n) = A081294(n+1) = A028403(n+1) - A000079(n+1) for n >=1. a(n-1) = 
               A028403(n) - A000079(n). [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), 
               Jul 27 2009]
%e A004171 For n=2, 9*8/8=3^2; n=8, 9*8^3/8=24^2; n=32, 9*32^3/8=192^2 [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Aug 05 2009]
%p A004171 seq(count(Subset(n))*count(Composition(n)),n=1..25); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Oct 16 2006
%p A004171 with(finance):seq(futurevalue(2,3,n), n=0..24);# [From Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Mar 25 2009]
%o A004171 (Other) sage: [lucas_number1(2*n, 2, 0) for n in xrange(1, 26)] # [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 27 2009]
%Y A004171 Absolute value of A009117. Essentially the same as A081294.
%Y A004171 A164632. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Aug 23 2009]
%Y A004171 Sequence in context: A145682 A099752 A081294 this_sequence A009117 A160637 
               A150829
%Y A004171 Adjacent sequences: A004168 A004169 A004170 this_sequence A004172 A004173 
               A004174
%K A004171 easy,nonn
%O A004171 0,1
%A A004171 N. J. A. Sloane (njas(AT)research.att.com).