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A029885 Boustrophedon transform of 1 followed by Thue-Morse sequence A001285.

%I A029885 #27 Jul 08 2025 19:24:34
%S A029885 1,2,5,13,34,108,415,1841,9381,53733,342086,2395481,18300250,
%T A029885 151453434,1349856656,12890177378,131298281746,1420980348324,
%U A029885 16283235530691,196958363484995,2507751773736087,33526171616091612
%N A029885 Boustrophedon transform of 1 followed by Thue-Morse sequence A001285.
%H A029885 Reinhard Zumkeller, <a href="/A029885/b029885.txt">Table of n, a(n) for n = 0..400</a>
%H A029885 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>.
%H A029885 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 A029885 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%H A029885 Wikipedia, <a href="https://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon transform</a>.
%H A029885 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%t A029885 tm[n_] := Mod[Sum[Mod[Binomial[n, k], 2], {k, 0, n}], 3];
%t A029885 T[n_, k_] := (n!/k!) SeriesCoefficient[(1 + Sin[x])/Cos[x], {x, 0, n - k}];
%t A029885 a[n_] := Sum[T[n, k] If[k == 0, 1, tm[k - 1]], {k, 0, n}];
%t A029885 Table[a[n], {n, 0, 21}] (* _Jean-François Alcover_, Jul 02 2019 *)
%o A029885 (Haskell)
%o A029885 a029885 n = sum $ zipWith (*) (a109449_row n) (1 : map fromIntegral a001285_list)
%o A029885 -- _Reinhard Zumkeller_, Nov 04 2013
%Y A029885 Cf. A109449, A001285, A230958, A230950, A230951.
%K A029885 nonn
%O A029885 0,2
%A A029885 _N. J. A. Sloane_
%E A029885 Definition corrected by _Reinhard Zumkeller_, Nov 04 2013