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

0,3

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

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

Example

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)

Maple

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

Crossrefs

Cf. A000045, A000738, A092073, A000744.

Sequence in context: A148454 A363042 A007743 * A085827 A347825 A150035

Adjacent sequences: A000684 A000685 A000686 * A000688 A000689 A000690

Keyword

nonn,changed

Author

N. J. A. Sloane and Simon Plouffe

Extensions

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

Status

approved