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.

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

Author

N. J. A. Sloane, May 12 2024, based on emails from Don Knuth, May 06 2024 and May 08 2024

Keywords

• nonn
• tabl

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.

Examples

			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, ...
   ...
		

Links

• D. E. Knuth, Notes on four arrays of numbers arising from the enumeration of CRC constraints and min-and-max-closed constraints, May 06 2024

Crossrefs

Cf. A099594, A100754, A272644, A372066, A372067.