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A000687 Boustrophedon transform (first version) of Fibonacci numbers 0,1,1,2,3,5,... 4
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

COMMENTS

The array begins:

................1.................

.............0..->..1.............

..........2..<-.2...<-..1.........

.......1..->.3..->..5...->..6.....

..17..<-.16..<-.13..<-..8...<-.2..

- John Cerkan, Jan 25 2017

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

MAPLE

read(transforms);

with(combinat):

F:=fibonacci;

[seq(F(n), n=0..50)];

BOUS(%);

CROSSREFS

Cf. A000045, A000738, A092073, A000744.

Sequence in context: A339223 A148454 A007743 * A085827 A150035 A000661

Adjacent sequences:  A000684 A000685 A000686 * A000688 A000689 A000690

KEYWORD

nonn

AUTHOR

N. J. A. Sloane and Simon Plouffe

EXTENSIONS

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

STATUS

approved

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Last modified June 15 18:33 EDT 2021. Contains 345049 sequences. (Running on oeis4.)