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A000687 Boustrophedon transform (first version) of Fibonacci numbers 0,1,1,2,3,5,...

%I A000687 #42 May 04 2024 05:31:52
%S A000687 1,1,2,6,17,59,229,1029,5242,30040,191201,1338897,10228097,84647981,
%T A000687 754437958,7204350870,73382899597,794189092567,9100736472725,
%U A000687 110080467183393,1401588037032782,18737851806495008,262435512896178877
%N A000687 Boustrophedon transform (first version) of Fibonacci numbers 0,1,1,2,3,5,...
%H A000687 John Cerkan, <a href="/A000687/b000687.txt">Table of n, a(n) for n = 0..482</a>
%H A000687 C. A. Church and M. Bicknell, <a href="https://www.mathstat.dal.ca/FQ/Scanned/11-3/church.pdf">Exponential generating functions for Fibonacci identities</a>, Fibonacci Quarterly, 11(3) (1973), 275-281.
%H A000687 J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory, 17A (1996) 44-54 (<a href="http://neilsloane.com/doc/bous.txt">Abstract</a>, <a href="http://neilsloane.com/doc/bous.pdf">pdf</a>, <a href="http://neilsloane.com/doc/bous.ps">ps</a>).
%H A000687 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A000687 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A000687 E.g.f.: (sec(x) + tan(x))*(((exp(a*x) - 1)/a - (exp(b*x) - 1)/b)/(a - b) + 1), where a = (1 + sqrt(5))/2 and b = (1 - sqrt(5))/2. - _Petros Hadjicostas_, Feb 16 2021
%e A000687 From _John Cerkan_, Jan 25 2017: (Start)
%e A000687 The array begins:
%e A000687                 1
%e A000687              0  ->  1
%e A000687           2  <- 2   <-  1
%e A000687        1  -> 3  ->  5   ->  6
%e A000687   17  <- 16  <- 13  <-  8   <- 2 (End)
%p A000687 read(transforms);
%p A000687 with(combinat):
%p A000687 F:=fibonacci;
%p A000687 [seq(F(n),n=0..50)];
%p A000687 BOUS(%);
%Y A000687 Cf. A000045, A000738, A092073, A000744.
%K A000687 nonn
%O A000687 0,3
%A A000687 _N. J. A. Sloane_ and _Simon Plouffe_
%E A000687 Entry revised by _N. J. A. Sloane_, Mar 15 2011