A000687 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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:

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)];