A092090 Boustrophedon transform of Fibonacci numbers 1, 2, 3, 5, 8, ...

1, 3, 8, 22, 67, 229, 897, 4023, 20512, 117516, 748031, 5237959, 40014097, 331156423, 2951484420, 28184585550, 287085799927, 3106996356945, 35603555478689, 430652619722011, 5483239453957132, 73305511708044652, 1026690239891085363, 15033060056592047307

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))*(a^2*exp(a*x) - b^2*exp(b*x))/(a - b), 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=2..30)]: BOUS2(a);

Prog

(Python)
from itertools import accumulate, islice
def A092090_gen(): # generator of terms
    blist, a, b = tuple(), 1, 2
    while True:
        yield (blist := tuple(accumulate(reversed(blist), initial=a)))[-1]
        a, b = b, a+b
A092090_list = list(islice(A092090_gen(), 40)) # Chai Wah Wu, Jun 12 2022

Crossrefs

Cf. A000744 (which uses BOUS2), A062122 (which uses Fibonacci numbers with an error in them), A092073.

Sequence in context: A003101 A064443 A000732 * A011958 A260661 A171841

Adjacent sequences: A092087 A092088 A092089 * A092091 A092092 A092093

Keyword

nonn

Author

N. J. A. Sloane, Apr 01 2004

Status

approved