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

1, 2, 5, 13, 34, 108, 415, 1841, 9381, 53733, 342086, 2395481, 18300250, 151453434, 1349856656, 12890177378, 131298281746, 1420980348324, 16283235530691, 196958363484995, 2507751773736087, 33526171616091612

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..400
• Peter Luschny, An old operation on sequences: the Seidel transform.
• 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 (Abstract, pdf, ps).
• N. J. A. Sloane, Transforms.
• Wikipedia, Boustrophedon transform.
• Index entries for sequences related to boustrophedon transform

Crossrefs

Cf. A109449, A001285, A230958, A230950, A230951.

Programs

Haskell

a029885 n = sum $ zipWith (*) (a109449_row n) (1 : map fromIntegral a001285_list)
-- Reinhard Zumkeller, Nov 04 2013

Mathematica

tm[n_] := Mod[Sum[Mod[Binomial[n, k], 2], {k, 0, n}], 3];
T[n_, k_] := (n!/k!) SeriesCoefficient[(1 + Sin[x])/Cos[x], {x, 0, n - k}];
a[n_] := Sum[T[n, k] If[k == 0, 1, tm[k - 1]], {k, 0, n}];
Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Jul 02 2019 *)

Extensions

Definition corrected by Reinhard Zumkeller, Nov 04 2013