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%I #26 Apr 21 2017 04:01:08
%S 0,1,1,1,0,1,1,0,0,1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,1,1,
%T 0,1,1,0,1,1,2,1,1,0,1,1,0,1,1,2,2,1,1,0,1,1,0,1,1,3,3,3,1,1,0,1,1,0,
%U 1,1,3,4,4,3,1,1,0,1,1,0,1,1,4,5,7,5,4,1,1,0,1
%N Table T(m, n) of number of (0, 1)-necklaces without zigzags with m 1's and n 0's, read by antidiagonals (see reference for precise definition).
%C See figure 2 on page 16 in the reference.
%C A zigzag is a substring which is either 010 or 101. The necklaces 01 and 10 are considered zigzags. Necklaces do not allow turnover.
%H Andrew Howroyd, <a href="/A263657/b263657.txt">Table of n, a(n) for n = 0..819</a>
%H E. Munarini and N. Z. Salvi, <a href="http://www.emis.de/journals/INTEGERS/papers/d19/d19.Abstract.html">Circular Binary Strings without Zigzags</a>, Integers: Electronic Journal of Combinatorial Number Theory 3 (2003), #A19.
%e Table starts:
%e 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ...
%e 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
%e 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ...
%e 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ...
%e 1 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 ...
%e 1 0 1 1 2 3 4 5 6 7 8 9 10 11 12 13 ...
%e 1 0 1 1 3 4 7 8 11 14 17 20 25 28 33 38 ...
%e 1 0 1 1 3 5 8 12 17 23 30 38 47 57 68 80 ...
%e 1 0 1 1 4 6 11 17 27 37 52 68 90 112 141 171 ...
%e 1 0 1 1 4 7 14 23 37 57 82 115 157 207 268 341 ...
%e 1 0 1 1 5 8 17 30 52 82 128 185 265 363 491 644 ...
%e 1 0 1 1 5 9 20 38 68 115 185 285 423 608 850 1160 ...
%Y Main diagonal is A263658. Antidiagonal sums are A263659.
%Y Cf. A007039, A263655, A263656.
%K nonn,tabl
%O 0,41
%A _Felix Fröhlich_, Oct 23 2015
%E a(45)-a(90) from _Andrew Howroyd_, Feb 26 2017
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