A080408 Boustrophedon transform of the continued fraction of e (A003417).

2, 3, 6, 14, 35, 116, 448, 1980, 10098, 57840, 368201, 2578384, 19697486, 163017000, 1452918806, 13874348700, 141322966623, 1529472867448, 17526468199148, 211996227034964, 2699219798770446, 36085910558435148, 505406091697374877

Offset

0,1

Links

Table of n, a(n) for n=0..22.

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

Formula

a(n) appears to be asymptotic to C*n!*(2/Pi)^n where C = 9.27921365277635263761227970562207183019110298580498662908878310... - Benoit Cloitre and Mark Hudson (mrmarkhudson(AT)hotmail.com)

Example

We simply apply the Boustrophedon transform to [2,1,2,1,1,4,1,1,6,1,1,8,1,1,...]

Prog

(Python)
from itertools import count, islice, accumulate
def A080408_gen(): # generator of terms
    blist = tuple()
    for n in count(1):
        yield (blist := tuple(accumulate(reversed(blist), initial=2 if n == 1 else 1 if n % 3 else n//3<<1)))[-1]
A080408_list = list(islice(A080408_gen(), 25)) # Chai Wah Wu, Jul 27 2022

Crossrefs

Cf. A003417, A001113, A080406, A080407.

Sequence in context: A002995 A093467 A246640 * A275774 A319323 A341630

Adjacent sequences: A080405 A080406 A080407 * A080409 A080410 A080411

Keyword

nonn,easy

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 17 2003

Status

approved