Search: id:A005183
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%I A005183 M1434
%S A005183 1,2,5,13,33,81,193,449,1025,2305,5121,11265,24577,53249,114689,245761,
%T A005183 524289,1114113,2359297,4980737,10485761,22020097,46137345,96468993,
%U A005183 201326593,419430401,872415233,1811939329,3758096385,7784628225
%N A005183 n*2^(n-1) + 1.
%C A005183 Number of permutations of length n which avoid the patterns 132, 4312. 
               - Lara Pudwell (Lara.Pudwell(AT)valpo.edu), Jan 21 2006
%D A005183 R. K. Guy, The second strong law of small numbers. Math. Mag. 63 (1990), 
               no. 1, 3-20.
%D A005183 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005183 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 A005183 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 A005183 Lara Pudwell, <a href="http://www.math.rutgers.edu/~lpudwell/webbook/
               bookmain.html">Systematic Studies in Pattern Avoidance</a>, 2005.
%F A005183 Main diagonal of the array defined by T(0, j)=j+1 j>=0, T(i, 0)=i+1 i>
               =0, T(i, j)=T(i-1, j-1)+T(i-1, j)-1 - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Jun 17 2003
%F A005183 G.f.: A(x) = -{x(3x^2-3x+1)}/{(x-1)(2x-1)^2} - Lara Pudwell (Lara.Pudwell(AT)valpo.edu), 
               Jan 21 2006
%F A005183 Binomial transform of A028310. a(n)=1+sum{k=0..n, C(n, k)k}=1+A001787(n) 
               - Paul Barry (pbarry(AT)wit.ie), Jul 21 2003
%F A005183 a(n) = sum(k=0, 2^n, A000120(k) ) = A000788(2^n) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Sep 25 2003
%F A005183 Row sums of triangle A134399 - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Oct 23 2007
%p A005183 A005183:=-(1-3*z+3*z**2)/(z-1)/(-1+2*z)**2; [Conjectured by S. Plouffe 
               in his 1992 dissertation.]
%t A005183 Table[(n+1)*2^n+1,{n,1,30}] - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Sep 09 2006
%Y A005183 Cf. A134399.
%Y A005183 Sequence in context: A027929 A001659 A088921 this_sequence A005348 A067676 
               A116703
%Y A005183 Adjacent sequences: A005180 A005181 A005182 this_sequence A005184 A005185 
               A005186
%K A005183 nonn,easy
%O A005183 0,2
%A A005183 N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy
%E A005183 More terms from Lara Pudwell (Lara.Pudwell(AT)valpo.edu), Jan 21 2006
%E A005183 Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion 
               of Jim Propp, Jul 14 2007

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