A080406 -id:A080406 - cp's OEIS frontend

A080407 Decimal expansion of the number which results when the Boustrophedon transform of the continued fraction of Pi (A080406, A001203) is interpreted as a continued fraction.

3, 0, 9, 9, 6, 8, 8, 6, 0, 6, 4, 0, 3, 0, 4, 8, 3, 4, 2, 5, 2, 6, 7, 2, 8, 8, 9, 1, 7, 2, 2, 0, 8, 8, 6, 6, 4, 1, 2, 8, 8, 7, 9, 7, 6, 0, 2, 5, 3, 0, 5, 4, 8, 8, 8, 1, 8, 5, 1, 2, 3, 5, 1, 3, 8, 9, 8, 0, 1, 1, 6, 5, 9, 4, 9, 4, 9, 5, 3, 4, 9, 3, 5, 1, 8, 0, 7, 4, 7, 2, 6, 1, 2, 2, 4, 4, 1, 1, 6, 6

Offset: 1

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

			3.0996886064030483425267288917220886641288...

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

Cf. A001203, A000796, A080406.

Offset corrected by R. J. Mathar, Feb 05 2009

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

Original entry on oeis.org

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

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

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

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

Cf. A003417, A001113, A080406, A080407.

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

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)

A080410 Boustrophedon transform of the continued fraction of the Euler-Mascheroni constant, gamma (A001620).

Original entry on oeis.org

0, 1, 3, 8, 23, 72, 279, 1236, 6313, 36133, 230119, 1611138, 12308693, 101865629, 907900133, 8669791288, 88309821406, 955736037556, 10951928988000, 132472073263683, 1686686835102650, 22549341913109430, 315817852408881670

Offset: 0

Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 18 2003

			We simply apply the Boustrophedon transform to [0,1,1,2,1,2,1,4,3,13,5,1,1,8,1,2,4,1,1,40,...] (A002852)

J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J.Combin. Theory, 17A 44-54 1996 (Abstract, pdf, ps).
N. J. A. Sloane, Transforms
Index entries for sequences related to boustrophedon transform

Cf. A001620, A002852, A080406-A080409.

a(n) appears to be asymptotic to C*n!*(2/Pi)^n where C=5.79838940503783299259552225238077705314049166104773668246015... which almost satisfies the polynomial equation 94487-16249C-8C^2=0 - Benoit Cloitre and Mark Hudson (mrmarkhudson(AT)hotmail.com)

cp's OEIS Frontend

A080407 Decimal expansion of the number which results when the Boustrophedon transform of the continued fraction of Pi (A080406, A001203) is interpreted as a continued fraction.

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

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A080410 Boustrophedon transform of the continued fraction of the Euler-Mascheroni constant, gamma (A001620).

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