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

0,3

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A230950, A230951.

Sequence in context: A259441 A176605 A080410 * A148777 A124462 A047857

Adjacent sequences: A230949 A230950 A230951 * A230953 A230954 A230955

Keyword

nonn

Author

Reinhard Zumkeller, Nov 03 2013

Status

approved