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

1, 1, 2, 6, 17, 59, 229, 1029, 5242, 30040, 191201, 1338897, 10228097, 84647981, 754437958, 7204350870, 73382899597, 794189092567, 9100736472725, 110080467183393, 1401588037032782, 18737851806495008, 262435512896178877

Offset: 0

Author

N. J. A. Sloane and Simon Plouffe

Keywords

• nonn

Examples

			From _John Cerkan_, Jan 25 2017: (Start)
The array begins:
                1
             0  ->  1
          2  <- 2   <-  1
       1  -> 3  ->  5   ->  6
  17  <- 16  <- 13  <-  8   <- 2 (End)
		

Links

• John Cerkan, Table of n, a(n) for n = 0..482
• C. A. Church and M. Bicknell, Exponential generating functions for Fibonacci identities, Fibonacci Quarterly, 11(3) (1973), 275-281.
• 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 (Abstract, pdf, ps).
• N. J. A. Sloane, Transforms
• Index entries for sequences related to boustrophedon transform

Crossrefs

Cf. A000045, A000738, A092073, A000744.

Programs

Maple

read(transforms);
with(combinat):
F:=fibonacci;
[seq(F(n),n=0..50)];
BOUS(%);

Formula

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

Extensions

Entry revised by N. J. A. Sloane, Mar 15 2011