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Boustrophedon transform of Hamming weight (A000120).
4

%I #17 Jun 12 2022 14:05:53

%S 0,1,3,8,23,72,280,1242,6331,36236,230726,1615584,12342422,102145644,

%T 910393530,8693609421,88552405435,958361506524,10982014291650,

%U 132835979792636,1691320230842116,22611285878526978,316685416851528722,4636988553066906265

%N Boustrophedon transform of Hamming weight (A000120).

%H Reinhard Zumkeller, <a href="/A230952/b230952.txt">Table of n, a(n) for n = 0..400</a>

%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>

%H 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 (<a href="http://neilsloane.com/doc/bous.txt">Abstract</a>, <a href="http://neilsloane.com/doc/bous.pdf">pdf</a>, <a href="http://neilsloane.com/doc/bous.ps">ps</a>).

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon transform</a>

%H <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>

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

%t T[n_, k_] := (n!/k!) SeriesCoefficient[(1 + Sin[x])/Cos[x], {x, 0, n - k}];

%t a[n_] := Sum[T[n, k] DigitCount[k, 2, 1], {k, 0, n}];

%t Table[a[n], {n, 0, 23}] (* _Jean-François Alcover_, Jul 23 2019 *)

%o (Haskell)

%o a230952 n = sum $ zipWith (*) (a109449_row n) $ map fromIntegral a000120_list

%o (Python 3.10+)

%o from itertools import accumulate, count, islice

%o def A230952_gen(): # generator of terms

%o blist = tuple()

%o for i in count(0):

%o yield (blist := tuple(accumulate(reversed(blist),initial=i.bit_count())))[-1]

%o A230952_list = list(islice(A230952_gen(),40)) # _Chai Wah Wu_, Jun 12 2022

%Y Cf. A230950, A230951.

%K nonn

%O 0,3

%A _Reinhard Zumkeller_, Nov 03 2013