A062122 Boustrophedon transform of 0, 1, 0, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,... the Fibonacci numbers (F_0 = 0, F_1 = 1, A000045) with an erroneous term (F_2 = 0 instead of 1).

0, 1, 2, 5, 19, 65, 259, 1161, 5927, 33946, 216090, 1513051, 11558614, 95658445, 852571616, 8141450460, 82928132445, 897492637757, 10284508144797, 124399102620413, 1583898570128385, 21175164077080102, 296571619014584968, 4342477201229994035, 66348164337987642924

Offset: 0

Author

Orleo Marinaro (KDNM21(AT)bipop.it), Jun 01 2001

Keywords

• nonn

Links

• 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

Programs

Maple

read transforms; with(combinat, fibonacci): a := [0,1,0,seq(fibonacci(i),i=3..30)]: BOUS2(a);

Formula

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

Extensions

Mar 31 2004: Thomas Sundquist noticed the original description was incorrect. Francisco Salinas was able to modify the description so as to produce the given sequence.