A230950 Boustrophedon transform of Thue-Morse sequence A010060.

0, 1, 3, 6, 15, 50, 186, 834, 4243, 24318, 154780, 1083952, 8280624, 68531308, 610796150, 5832677415, 59411150931, 642979374958, 7368000716808, 89121684577460, 1134732527849730, 15170256449030866, 212469074496520610, 3111026318662704255, 47532980801984327584

Offset: 0

Author

Reinhard Zumkeller, Nov 03 2013

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 44-54 1996 (Abstract, pdf, ps).
• Wikipedia, Boustrophedon transform
• Index entries for sequences related to boustrophedon transform

Crossrefs

Cf. A029885, A230951, A230952.

Cf. A010060, A109449.

Programs

Haskell

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

Mathematica

T[n_, k_] := (n!/k!) SeriesCoefficient[(1 + Sin[x])/Cos[x], {x, 0, n - k}];
a[n_] := Sum[T[n, k] ThueMorse[k], {k, 0, n}];
Table[a[n], {n, 0, 24}] (* Jean-François Alcover, Jul 02 2019 *)

Python

from itertools import count, islice, accumulate
def A230950_gen(): # generator of terms
    blist = tuple()
    for i in count(0):
        yield (blist := tuple(accumulate(reversed(blist), initial=i.bit_count()&1)))[-1]
A230950_list = list(islice(A230950_gen(),30)) # Chai Wah Wu, Apr 17 2023

Formula

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