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A372068
Array read by antidiagonals: T(m,n) (m >= 0, n >= 0) = number of max-and-min-closed constraints between an m-element set and an n-element set.
3
1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 8, 13, 8, 1, 1, 16, 38, 38, 16, 1, 1, 32, 104, 147, 104, 32, 1, 1, 64, 272, 506, 506, 272, 64, 1, 1, 128, 688, 1612, 2103, 1612, 688, 128, 1, 1, 256, 1696, 4856, 7887, 7887, 4856, 1696, 256, 1, 1, 512, 4096, 14016, 27477, 34088, 27477, 14016, 4096, 512, 1
OFFSET
0,5
COMMENTS
See the Knuth "Notes" link for much more information about these sequences. The present sequence is called "tab" in Part 2 of the Notes.
EXAMPLE
The initial antidiagonals are:
1,
1, 1,
1, 2, 1,
1, 4, 4, 1,
1, 8, 13, 8, 1,
1, 16, 38, 38, 16, 1,
1, 32, 104, 147, 104, 32, 1,
1, 64, 272, 506, 506, 272, 64, 1,
1, 128, 688, 1612, 2103, 1612, 688, 128, 1,
1, 256, 1696, 4856, 7887, 7887, 4856, 1696, 256, 1,
1, 512, 4096, 14016, 27477, 34088, 27477, 14016, 4096, 512, 1,
...
The array begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, ...
1, 4, 13, 38, 104, 272, 688, 1696, 4096, 9728, ...
1, 8, 38, 147, 506, 1612, 4856, 14016, 39104, 106112, ...
1, 16, 104, 506, 2103, 7887, 27477, 90498, 285072, 865856, ...
1, 32, 272, 1612, 7887, 34088, 134825, 498465, 1746830, 5859404, ...
1, 64, 688, 4856, 27477, 134825, 597539, 2451038, 9455182, 34687916, ...
1, 128, 1696, 14016, 90498, 498465, 2451038, 11055950, 46570858, 185484836, ...
1, 256, 4096, 39104, 285072, 1746830, 9455182, 46570858, 212833803, 914854829, ...
1, 512, 9728, 106112, 865856, 5859404, 34687916, 185484836, 914854829, 4223468802, ...
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, May 12 2024, based on emails from Don Knuth, May 06 2024 and May 08 2024
STATUS
approved