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%I #46 Jun 12 2022 12:01:54
%S 1,1,2,5,12,41,152,685,3472,19921,126752,887765,6781632,56126201,
%T 500231552,4776869245,48656756992,526589630881,6034272215552,
%U 72989204937125,929327412759552,12424192360405961,174008703107274752
%N Boustrophedon transform of (n+1) mod 2.
%H Reinhard Zumkeller, <a href="/A062272/b062272.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 Ser. A, 76(1) (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 J. Millar, N. J. A. Sloane, and N. E. Young, <a href="https://doi.org/10.1006/jcta.1996.0087">A new operation on sequences: the Boustrophedon transform</a>, J. Combin. Theory Ser. A, 76(1) (1996), 44-54.
%H Ludwig Seidel, <a href="https://babel.hathitrust.org/cgi/pt?id=hvd.32044092897461&view=1up&seq=175">Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen</a>, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [USA access only through the <a href="https://www.hathitrust.org/accessibility">HATHI TRUST Digital Library</a>]
%H Ludwig Seidel, <a href="https://www.zobodat.at/pdf/Sitz-Ber-Akad-Muenchen-math-Kl_1877_0157-0187.pdf">Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen</a>, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [Access through <a href="https://de.wikipedia.org/wiki/ZOBODAT">ZOBODAT</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 E.g.f.: (sec(x)+tan(x))cosh(x); a(n)=(A000667(n)+A062162(n))/2. - _Paul Barry_, Jan 21 2005
%F a(n) = Sum{k, k>=0} binomial(n, 2k)*A000111(n-2k). - _Philippe Deléham_, Aug 28 2005
%F a(n) = sum(A109449(n,k) * (1 - n mod 2): k=0..n). - _Reinhard Zumkeller_, Nov 03 2013
%t s[n_] = Mod[n+1, 2]; t[n_, 0] := s[n]; 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 (Sage) # Generalized algorithm of L. Seidel (1877)
%o def A062272_list(n) :
%o R = []; A = {-1:0, 0:0}
%o k = 0; e = 1
%o for i in range(n) :
%o Am = 1 if e == 1 else 0
%o A[k + e] = 0
%o e = -e
%o for j in (0..i) :
%o Am += A[k]
%o A[k] = Am
%o k += e
%o R.append(A[e*i//2])
%o return R
%o A062272_list(10) # _Peter Luschny_, Jun 02 2012
%o (Haskell)
%o a062272 n = sum $ zipWith (*) (a109449_row n) $ cycle [1,0]
%o -- _Reinhard Zumkeller_, Nov 03 2013
%o (Python)
%o from itertools import accumulate, islice
%o def A062272_gen(): # generator of terms
%o blist, m = tuple(), 0
%o while True:
%o yield (blist := tuple(accumulate(reversed(blist),initial=(m := 1-m))))[-1]
%o A062272_list = list(islice(A062272_gen(),40)) # _Chai Wah Wu_, Jun 12 2022
%Y A000734 (binomial transform), a(2n+1)= A003719(n), a(2n)= A000795(n),
%Y Cf. A062161 (n mod 2).
%Y Row sums of A162170 minus A000035. - _Mats Granvik_, Jun 27 2009
%Y Cf. A059841.
%K nonn,easy
%O 0,3
%A _Frank Ellermann_, Jun 16 2001
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