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A058257 Triangle read by rows: this is a variant of A008280 in which 2 rows go from left to right, 2 from right to left, 2 from left to right, etc.

%I A058257 #15 Feb 18 2021 00:43:13
%S A058257 1,0,1,0,0,1,1,1,1,0,3,2,1,0,0,0,3,5,6,6,6,0,0,3,8,14,20,26,71,71,71,
%T A058257 68,60,46,26,0,413,342,271,200,132,72,26,0,0,0,413,755,1026,1226,1358,
%U A058257 1430,1456,1456,1456,0,0,413,1168,2194,3420,4778,6208,7664,9120,10576
%N A058257 Triangle read by rows: this is a variant of A008280 in which 2 rows go from left to right, 2 from right to left, 2 from left to right, etc.
%C A058257 Suggested by Atkinson article in Information Processing Letters.
%D A058257 M. D. Atkinson, Partial orders and comparison problems, Sixteenth Southeastern Conference on Combinatorics, Graph Theory and Computing, (Boca Raton, Feb 1985), Congressus Numerantium 47, 77-88.
%H A058257 Reinhard Zumkeller, <a href="/A058257/b058257.txt">Rows n = 0..120 of triangle, flattened</a>
%H A058257 M. D. Atkinson, <a href="https://doi.org/10.1016/0020-0190(85)90057-2">Zigzag permutations and comparisons of adjacent elements</a>, Information Processing Letters 21 (1985), 187-189.
%H A058257 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 A058257 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%e A058257 Triangle begins:
%e A058257   1;
%e A058257   0, 1;
%e A058257   0, 0, 1;
%e A058257   1, 1, 1, 0;
%e A058257   3, 2, 1, 0, 0;
%e A058257   0, 3, 5, 6, 6, 6;
%e A058257   ...
%o A058257 (Haskell)
%o A058257 a058257 n k = a058257_tabl !! n !! k
%o A058257 a058257_row n = a058257_tabl !! n
%o A058257 a058257_tabl = [1] : ox 0 [1] where
%o A058257    ox turn xs = ys : ox (mod (turn + 1) 4) ys
%o A058257       where ys | turn <= 1 = scanl (+) 0 xs
%o A058257                | otherwise = reverse $ scanl (+) 0 $ reverse xs
%o A058257 -- _Reinhard Zumkeller_, Nov 01 2013
%Y A058257 Cf. A058258, A008280, A000111.
%K A058257 nonn,easy,tabl,nice
%O A058257 0,11
%A A058257 _N. J. A. Sloane_, Dec 06 2000
%E A058257 More terms from Larry Reeves (larryr(AT)acm.org), Dec 12 2000