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
Examples
We simply apply the Boustrophedon transform to [2,1,2,1,1,4,1,1,6,1,1,8,1,1,...]
Links
- 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
Programs
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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
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)