A230952 Boustrophedon transform of Hamming weight (A000120).

0, 1, 3, 8, 23, 72, 280, 1242, 6331, 36236, 230726, 1615584, 12342422, 102145644, 910393530, 8693609421, 88552405435, 958361506524, 10982014291650, 132835979792636, 1691320230842116, 22611285878526978, 316685416851528722, 4636988553066906265

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. A230950, A230951.

Programs

Haskell

a230952 n = sum $ zipWith (*) (a109449_row n) $ map fromIntegral a000120_list
(Python 3.10+)
from itertools import accumulate, count, islice
def A230952_gen(): # generator of terms
        blist = tuple()
        for i in count(0):
            yield (blist := tuple(accumulate(reversed(blist),initial=i.bit_count())))[-1]
A230952_list = list(islice(A230952_gen(),40)) # Chai Wah Wu, Jun 12 2022

Mathematica

T[n_, k_] := (n!/k!) SeriesCoefficient[(1 + Sin[x])/Cos[x], {x, 0, n - k}];
a[n_] := Sum[T[n, k] DigitCount[k, 2, 1], {k, 0, n}];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Jul 23 2019 *)

Formula

a(n) = Sum_{k=0..n} A109449(n,k)*A000120(k).