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Boustrophedon transform of Thue-Morse sequence A001285.
3

%I #29 Apr 18 2023 08:28:57

%S 1,3,7,15,39,127,480,2143,10907,62495,397814,2785861,21282228,

%T 176133285,1569817724,14990658724,152693582275,1652531857935,

%U 18936620009722,229053108410969,2916394751599614,38989325834726043,546070266163669664,7995699956778626764

%N Boustrophedon transform of Thue-Morse sequence A001285.

%H Reinhard Zumkeller, <a href="/A230958/b230958.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 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 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 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 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 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)*A001285(k).

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

%t tm[n_] := Mod[Sum[Mod[Binomial[n, k], 2], {k, 0, n}], 3];

%t Table[Sum[T[n, k] tm[k], {k, 0, n}], {n, 0, 23}] (* _Jean-François Alcover_, Jul 23 2019 *)

%o (Haskell)

%o a230958 n = sum $ zipWith (*) (a109449_row n) $ map fromIntegral a001285_list

%o (Python)

%o from itertools import accumulate, count, islice

%o def A230958_gen(): # generator of terms

%o blist = tuple()

%o for i in count(0):

%o yield (blist := tuple(accumulate(reversed(blist), initial=2 if i.bit_count()&1 else 1)))[-1]

%o A230958_list = list(islice(A230958_gen(),30)) # _Chai Wah Wu_, Apr 17 2023

%Y Cf. A029885, A230950, A230951.

%Y Cf. A001285, A109449.

%K nonn

%O 0,2

%A _Reinhard Zumkeller_, Nov 04 2013