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A263657
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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).
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5
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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, 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, 1, 1, 3, 4, 4, 3, 1, 1, 0, 1, 1, 0, 1, 1, 4, 5, 7, 5, 4, 1, 1, 0, 1
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OFFSET
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0,41
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COMMENTS
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See figure 2 on page 16 in the reference.
A zigzag is a substring which is either 010 or 101. The necklaces 01 and 10 are considered zigzags. Necklaces do not allow turnover.
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LINKS
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EXAMPLE
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Table starts:
0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ...
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ...
1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ...
1 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 ...
1 0 1 1 2 3 4 5 6 7 8 9 10 11 12 13 ...
1 0 1 1 3 4 7 8 11 14 17 20 25 28 33 38 ...
1 0 1 1 3 5 8 12 17 23 30 38 47 57 68 80 ...
1 0 1 1 4 6 11 17 27 37 52 68 90 112 141 171 ...
1 0 1 1 4 7 14 23 37 57 82 115 157 207 268 341 ...
1 0 1 1 5 8 17 30 52 82 128 185 265 363 491 644 ...
1 0 1 1 5 9 20 38 68 115 185 285 423 608 850 1160 ...
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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