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%I #45 Jun 13 2022 03:02:52
%S 1,2,4,10,30,101,394,1760,8970,51368,326991,2289669,17491625,
%T 144760655,1290204758,12320541392,125496010615,1358185050788,
%U 15563654383395,188254471337718,2396930376564860,32044598671291610
%N Boustrophedon transform of partition numbers 1, 1, 1, 2, 3, 5, 7, ...
%H John Cerkan, <a href="/A000733/b000733.txt">Table of n, a(n) for n = 0..482</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 (1996) 44-54 (<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 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon transform</a>.
%H <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%e The array begins:
%e 1
%e 1 -> 2
%e 4 <- 3 <- 1
%e 2 -> 6 -> 9 -> 10
%e 30 <- 28 <- 22 <- 13 <- 3
%e - _John Cerkan_, Jan 26 2017
%t t[n_, 0] := If[n == 0, 1, PartitionsP[n-1]]; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n-1, n-k]; a[n_] := t[n, n]; Array[a, 30, 0] (* _Jean-François Alcover_, Feb 12 2016 *)
%o (Haskell)
%o a000733 n = sum $ zipWith (*) (a109449_row n) (1 : a000041_list)
%o -- _Reinhard Zumkeller_, Nov 04 2013
%o (Python)
%o from itertools import count, accumulate, islice
%o from sympy import npartitions
%o def A000733_gen(): # generator of terms
%o yield 1
%o blist = (1,)
%o for i in count(0):
%o yield (blist := tuple(accumulate(reversed(blist),initial=npartitions(i))))[-1]
%o A000733_list = list(islice(A000733_gen(),40)) # _Chai Wah Wu_, Jun 12 2022
%Y Cf. A000041, A000751, A109449, A230957.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, _Simon Plouffe_
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