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Boustrophedon transform of Thue-Morse sequence A010060.
5

%I #19 Apr 18 2023 07:39:11

%S 0,1,3,6,15,50,186,834,4243,24318,154780,1083952,8280624,68531308,

%T 610796150,5832677415,59411150931,642979374958,7368000716808,

%U 89121684577460,1134732527849730,15170256449030866,212469074496520610,3111026318662704255,47532980801984327584

%N Boustrophedon transform of Thue-Morse sequence A010060.

%H Reinhard Zumkeller, <a href="/A230950/b230950.txt">Table of n, a(n) for n = 0..400</a>

%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>

%H 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 (<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 Wikipedia, <a href="http://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon transform</a>

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

%F a(n) = Sum_{k=0..n} A109449(n,k)*A010060(k).

%t T[n_, k_] := (n!/k!) SeriesCoefficient[(1 + Sin[x])/Cos[x], {x, 0, n - k}];

%t a[n_] := Sum[T[n, k] ThueMorse[k], {k, 0, n}];

%t Table[a[n], {n, 0, 24}] (* _Jean-François Alcover_, Jul 02 2019 *)

%o (Haskell)

%o a230950 n = sum $ zipWith (*) (a109449_row n) $ map fromIntegral a010060_list

%o (Python)

%o from itertools import count, islice, accumulate

%o def A230950_gen(): # generator of terms

%o blist = tuple()

%o for i in count(0):

%o yield (blist := tuple(accumulate(reversed(blist), initial=i.bit_count()&1)))[-1]

%o A230950_list = list(islice(A230950_gen(),30)) # _Chai Wah Wu_, Apr 17 2023

%Y Cf. A029885, A230951, A230952.

%Y Cf. A010060, A109449.

%K nonn

%O 0,3

%A _Reinhard Zumkeller_, Nov 03 2013