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Boustrophedon transform (first version) of Fibonacci numbers 1, 1, 2, 3, 5, 8, ...
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%I #24 Feb 17 2021 07:34:46

%S 1,2,4,10,30,101,395,1769,9020,51674,328936,2303323,17595765,

%T 145622477,1297884212,12393874652,126242962310,1366268975165,

%U 15656289178423,189374961382141,2411196896699700,32235328003898918,451476237890591144,6610630095177242675

%N Boustrophedon transform (first version) of Fibonacci numbers 1, 1, 2, 3, 5, 8, ...

%H 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 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 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.

%F E.g.f.: (sec(x) + tan(x))*((exp(a*x) - exp(b*x))/(a - b) + 1), where a = (1 + sqrt(5))/2 and b = (1 - sqrt(5))/2. - _Petros Hadjicostas_, Feb 16 2021

%p read transforms; with(combinat, fibonacci): a := [seq(fibonacci(i),i=1..50)]: BOUS(a);

%Y Cf. A000687, A000738, A000744 (which uses BOUS2), A062122 (which uses Fibonacci numbers with an error in them), A092090.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Apr 01 2004

%E Entry revised by _N. J. A. Sloane_, Mar 16 2011