A062122 -id:A062122 - cp's OEIS frontend

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

N. J. A. Sloane, Apr 01 2004

nonn

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.

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

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

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

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

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

Original entry on oeis.org

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

N. J. A. Sloane, Apr 01 2004

nonn

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.

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

read transforms; with(combinat, fibonacci): a := [seq(fibonacci(i),i=2..30)]: BOUS2(a);

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

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

cp's OEIS Frontend

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

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Formula

Extensions