A230951 Boustrophedon transform of Thue-Morse sequence A010059.

1, 1, 1, 3, 9, 27, 108, 475, 2421, 13859, 88254, 617957, 4720980, 39070669, 348225424, 3325303894, 33871280413, 366573108019, 4200618576106, 50809739256049, 646929695900154, 8648812936664311, 121132117170628444, 1773647319453218254, 27099334868109293640

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, A230950, A230952.

Cf. A010059, A109449.

Programs

Haskell

a230951 n = sum $ zipWith (*) (a109449_row n) $ map fromIntegral a010059_list

Python

from itertools import count, islice, accumulate
def A230951_gen(): # generator of terms
    blist = tuple()
    for i in count(0):
        yield (blist := tuple(accumulate(reversed(blist), initial=i.bit_count()&1^1)))[-1]
A230951_list = list(islice(A230951_gen(),30)) # Chai Wah Wu, Apr 17 2023

Formula

a(n) = Sum_{k=0..n} A109449(n,k)*A010059(k).