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A230952 Boustrophedon transform of Hamming weight (A000120).

%I A230952 #17 Jun 12 2022 14:05:53
%S A230952 0,1,3,8,23,72,280,1242,6331,36236,230726,1615584,12342422,102145644,
%T A230952 910393530,8693609421,88552405435,958361506524,10982014291650,
%U A230952 132835979792636,1691320230842116,22611285878526978,316685416851528722,4636988553066906265
%N A230952 Boustrophedon transform of Hamming weight (A000120).
%H A230952 Reinhard Zumkeller, <a href="/A230952/b230952.txt">Table of n, a(n) for n = 0..400</a>
%H A230952 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>
%H A230952 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 A230952 Wikipedia, <a href="http://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon transform</a>
%H A230952 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A230952 a(n) = Sum_{k=0..n} A109449(n,k)*A000120(k).
%t A230952 T[n_, k_] := (n!/k!) SeriesCoefficient[(1 + Sin[x])/Cos[x], {x, 0, n - k}];
%t A230952 a[n_] := Sum[T[n, k] DigitCount[k, 2, 1], {k, 0, n}];
%t A230952 Table[a[n], {n, 0, 23}] (* _Jean-François Alcover_, Jul 23 2019 *)
%o A230952 (Haskell)
%o A230952 a230952 n = sum $ zipWith (*) (a109449_row n) $ map fromIntegral a000120_list
%o A230952 (Python 3.10+)
%o A230952 from itertools import accumulate, count, islice
%o A230952 def A230952_gen(): # generator of terms
%o A230952         blist = tuple()
%o A230952         for i in count(0):
%o A230952             yield (blist := tuple(accumulate(reversed(blist),initial=i.bit_count())))[-1]
%o A230952 A230952_list = list(islice(A230952_gen(),40)) # _Chai Wah Wu_, Jun 12 2022
%Y A230952 Cf. A230950, A230951.
%K A230952 nonn
%O A230952 0,3
%A A230952 _Reinhard Zumkeller_, Nov 03 2013