A092073 Boustrophedon transform (first version) of Fibonacci numbers 1, 1, 2, 3, 5, 8, ...

1, 2, 4, 10, 30, 101, 395, 1769, 9020, 51674, 328936, 2303323, 17595765, 145622477, 1297884212, 12393874652, 126242962310, 1366268975165, 15656289178423, 189374961382141, 2411196896699700, 32235328003898918, 451476237890591144, 6610630095177242675

Offset: 0

Author

N. J. A. Sloane, Apr 01 2004

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.

Crossrefs

Cf. A000687, A000738, A000744 (which uses BOUS2), A062122 (which uses Fibonacci numbers with an error in them), A092090.

Programs

Maple

read transforms; with(combinat, fibonacci): a := [seq(fibonacci(i),i=1..50)]: BOUS(a);

Formula

E.g.f.: (sec(x) + tan(x))*((exp(a*x) - exp(b*x))/(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 16 2011