cp's OEIS Frontend

A263657 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).

%I A263657 #26 Apr 21 2017 04:01:08
%S A263657 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 A263657 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 A263657 1,1,3,4,4,3,1,1,0,1,1,0,1,1,4,5,7,5,4,1,1,0,1
%N A263657 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 A263657 See figure 2 on page 16 in the reference.
%C A263657 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 A263657 Andrew Howroyd, <a href="/A263657/b263657.txt">Table of n, a(n) for n = 0..819</a>
%H A263657 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 A263657 Table starts:
%e A263657 0 1 1 1 1  1  1  1   1   1   1    1    1    1    1    1 ...
%e A263657 1 0 0 0 0  0  0  0   0   0   0    0    0    0    0    0 ...
%e A263657 1 0 1 1 1  1  1  1   1   1   1    1    1    1    1    1 ...
%e A263657 1 0 1 1 1  1  1  1   1   1   1    1    1    1    1    1 ...
%e A263657 1 0 1 1 2  2  3  3   4   4   5    5    6    6    7    7 ...
%e A263657 1 0 1 1 2  3  4  5   6   7   8    9   10   11   12   13 ...
%e A263657 1 0 1 1 3  4  7  8  11  14  17   20   25   28   33   38 ...
%e A263657 1 0 1 1 3  5  8 12  17  23  30   38   47   57   68   80 ...
%e A263657 1 0 1 1 4  6 11 17  27  37  52   68   90  112  141  171 ...
%e A263657 1 0 1 1 4  7 14 23  37  57  82  115  157  207  268  341 ...
%e A263657 1 0 1 1 5  8 17 30  52  82 128  185  265  363  491  644 ...
%e A263657 1 0 1 1 5  9 20 38  68 115 185  285  423  608  850 1160 ...
%Y A263657 Main diagonal is A263658. Antidiagonal sums are A263659.
%Y A263657 Cf. A007039, A263655, A263656.
%K A263657 nonn,tabl
%O A263657 0,41
%A A263657 _Felix Fröhlich_, Oct 23 2015
%E A263657 a(45)-a(90) from _Andrew Howroyd_, Feb 26 2017