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A230958 Boustrophedon transform of Thue-Morse sequence A001285.

%I A230958 #29 Apr 18 2023 08:28:57
%S A230958 1,3,7,15,39,127,480,2143,10907,62495,397814,2785861,21282228,
%T A230958 176133285,1569817724,14990658724,152693582275,1652531857935,
%U A230958 18936620009722,229053108410969,2916394751599614,38989325834726043,546070266163669664,7995699956778626764
%N A230958 Boustrophedon transform of Thue-Morse sequence A001285.
%H A230958 Reinhard Zumkeller, <a href="/A230958/b230958.txt">Table of n, a(n) for n = 0..400</a>
%H A230958 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>.
%H A230958 J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory Ser. A, 76(1) (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 A230958 J. Millar, N. J. A. Sloane and N. E. Young, <a href="https://doi.org/10.1006/jcta.1996.0087">A new operation on sequences: the Boustrophedon transform</a>, J. Combin. Theory Ser. A, 76(1) (1996), 44-54.
%H A230958 Ludwig Seidel, <a href="https://babel.hathitrust.org/cgi/pt?id=hvd.32044092897461&amp;view=1up&amp;seq=175">Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen</a>, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [USA access only through the <a href="https://www.hathitrust.org/accessibility">HATHI TRUST Digital Library</a>]
%H A230958 Ludwig Seidel, <a href="https://www.zobodat.at/pdf/Sitz-Ber-Akad-Muenchen-math-Kl_1877_0157-0187.pdf">Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen</a>, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [Access through <a href="https://de.wikipedia.org/wiki/ZOBODAT">ZOBODAT</a>]
%H A230958 Wikipedia, <a href="http://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon transform</a>.
%H A230958 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A230958 a(n) = Sum_{k=0..n} A109449(n,k)*A001285(k).
%t A230958 T[n_, k_] := (n!/k!) SeriesCoefficient[(1 + Sin[x])/Cos[x], {x, 0, n - k}];
%t A230958 tm[n_] := Mod[Sum[Mod[Binomial[n, k], 2], {k, 0, n}], 3];
%t A230958 Table[Sum[T[n, k] tm[k], {k, 0, n}], {n, 0, 23}] (* _Jean-François Alcover_, Jul 23 2019 *)
%o A230958 (Haskell)
%o A230958 a230958 n = sum $ zipWith (*) (a109449_row n) $ map fromIntegral a001285_list
%o A230958 (Python)
%o A230958 from itertools import accumulate, count, islice
%o A230958 def A230958_gen(): # generator of terms
%o A230958     blist = tuple()
%o A230958     for i in count(0):
%o A230958         yield (blist := tuple(accumulate(reversed(blist), initial=2 if i.bit_count()&1 else 1)))[-1]
%o A230958 A230958_list = list(islice(A230958_gen(),30)) # _Chai Wah Wu_, Apr 17 2023
%Y A230958 Cf. A029885, A230950, A230951.
%Y A230958 Cf. A001285, A109449.
%K A230958 nonn
%O A230958 0,2
%A A230958 _Reinhard Zumkeller_, Nov 04 2013