Search: id:A000667
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%I A000667
%S A000667 1,2,4,9,24,77,294,1309,6664,38177,243034,1701909,13001604,
%T A000667 107601977,959021574,9157981309,93282431344,1009552482977,
%U A000667 11568619292914,139931423833509,1781662223749884,23819069385695177
%N A000667 Boustrophedon transform of all-1's sequence.
%C A000667 Fill in a triangle, like Pascal's triangle, beginning each row with a 
               1 and filling in rows alternately right to left and left to right. 
               Thus:
%C A000667 ...............1.............
%C A000667 ............1..->..2..........
%C A000667 .........4..<-.3...<-..1......
%C A000667 ......1..->.5..->..8...->..9..
%C A000667 ..............................
%H A000667 T. D. Noe, <a href="b000667.txt">Table of n, a(n) for n=0..100</a>
%H A000667 J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: 
               the Boustrophedon on transform, J. Combin. Theory, 17A 44-54 1996 
               (<a href="http://www.research.att.com/~njas/doc/bous.txt">Abstract</
               a>, <a href="http://www.research.att.com/~njas/doc/bous.pdf">pdf</
               a>, <a href="http://www.research.att.com/~njas/doc/bous.ps">ps</a>
               ).
%H A000667 N. J. A. Sloane, <a href="http://www.research.att.com/~njas/doc/sg.txt">
               My favorite integer sequences</a>, in Sequences and their Applications 
               (Proceedings of SETA '98).
%H A000667 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%H A000667 <a href="Sindx_Bo.html#boustrophedon">Index entries for sequences related 
               to boustrophedon transform</a>
%F A000667 E.g.f.: exp(x) (tan x + sec x).
%F A000667 Lim n->infinity 2*n*a(n-1)/a(n) = Pi; lim n->infinity a(n)*a(n-2)/a(n-1)^2 
               = 1 + 1/(n-1) - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), 
               Aug 13 2004
%F A000667 a(n) = Sum_{k, k>=0} binomial(n, k)*A000111(n-k) . a(2n) = A000795(n) 
               + A009747(n), a(2n+1) = A002084(n) + A003719(n) . - Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Aug 28 2005
%Y A000667 Absolute value of pairwise sums of A009337.
%Y A000667 Sequence in context: A005001 A091151 A093542 this_sequence A131351 A091352 
               A135934
%Y A000667 Adjacent sequences: A000664 A000665 A000666 this_sequence A000668 A000669 
               A000670
%K A000667 nonn,easy,nice
%O A000667 0,2
%A A000667 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)

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