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

0,2

Links

Table of n, a(n) for n=0..23.

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.

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

Maple

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

Crossrefs

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

Sequence in context: A007558 A094957 A000733 * A274232 A360322 A112846

Adjacent sequences: A092070 A092071 A092072 * A092074 A092075 A092076

Keyword

nonn

Author

N. J. A. Sloane, Apr 01 2004

Extensions

Entry revised by N. J. A. Sloane, Mar 16 2011

Status

approved