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Boustrophedon transform of the continued fraction of e (A003417).
1

%I #20 Jul 28 2022 09:06:41

%S 2,3,6,14,35,116,448,1980,10098,57840,368201,2578384,19697486,

%T 163017000,1452918806,13874348700,141322966623,1529472867448,

%U 17526468199148,211996227034964,2699219798770446,36085910558435148,505406091697374877

%N Boustrophedon transform of the continued fraction of e (A003417).

%H 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 (<a href="http://neilsloane.com/doc/bous.txt">Abstract</a>, <a href="http://neilsloane.com/doc/bous.pdf">pdf</a>, <a href="http://neilsloane.com/doc/bous.ps">ps</a>).

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>

%F 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)

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

%o (Python)

%o from itertools import count, islice, accumulate

%o def A080408_gen(): # generator of terms

%o blist = tuple()

%o for n in count(1):

%o yield (blist := tuple(accumulate(reversed(blist),initial=2 if n == 1 else 1 if n % 3 else n//3<<1)))[-1]

%o A080408_list = list(islice(A080408_gen(),25)) # _Chai Wah Wu_, Jul 27 2022

%Y Cf. A003417, A001113, A080406, A080407.

%K nonn,easy

%O 0,1

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