A372066 - OEIS

%I #29 May 15 2024 16:38:04

%S 1,1,1,1,7,1,1,17,17,1,1,31,90,31,1,1,49,284,284,49,1,1,71,687,1398,

%T 687,71,1,1,97,1411,4861,4861,1411,97,1,1,127,2592,13555,23020,13555,

%U 2592,127,1,1,161,4390,32436,83858,83858,32436,4390,161,1

%N Array read by antidiagonals: T(m,n) (m >= 1, n >= 1) = number of reduced connected row convex (RCRC) constraints between an m-element set and an n-element set.

%C See the Knuth "Notes" link for much more information about these sequences. The present sequence is called "table0" in Part 1 of the Notes.

%D Yves Deville, Olivier Barette, Pascal Van Hentenryck, Constraint satisfaction over connected row-convex constraints, Artificial Intelligence 109 (1999), 243-271.

%D Peter Jeavons, David Cohen, Martin C. Cooper, Constraints, consistency and closure". Artificial Intelligence 101 (1998), 251-265.

%H D. E. Knuth, <a href="/A372066/a372066.txt">Notes on four arrays of numbers arising from the enumeration of CRC constraints and min-and-max-closed constraints</a>, May 06 2024

%F Knuth gives a formula expressing the array A372367 in terms of the current array. He also reports that there is strong experimental evidence that the n-th term of row m in the current array is a polynomial of degree 2*m-2 in n.

%e The initial antidiagonals are:

%e    1,

%e    1, 1,

%e    1, 7, 1,

%e    1, 17, 17, 1,

%e    1, 31, 90, 31, 1,

%e    1, 49, 284, 284, 49, 1,

%e    1, 71, 687, 1398, 687, 71, 1,

%e    1, 97, 1411, 4861, 4861, 1411, 97, 1,

%e    1, 127, 2592, 13555, 23020, 13555, 2592, 127, 1,

%e    1, 161, 4390, 32436, 83858, 83858, 32436, 4390, 161, 1,

%e    ...

%e The array begins:

%e    1, 1, 1, 1, 1, 1, 1, 1, 1, ...

%e    1, 7, 17, 31, 49, 71, 97, 127, 161, ...

%e    1, 17, 90, 284, 687, 1411, 2592, 4390, 6989, ...

%e    1, 31, 284, 1398, 4861, 13555, 32436, 69350, 135985, ...

%e    1, 49, 687, 4861, 23020, 83858, 253876, 669660, 1587491, ...

%e    1, 71, 1411, 13555, 83858, 386774, 1445748, 4613486, 13010537, ...

%e    1, 97, 2592, 32436, 253876, 1445748, 6539320, 24831150, 82162821, ...

%e    1, 127, 4390, 69350, 669660, 4613486, 24831150, 110639796, 424473531, ...

%e    1, 161, 6989, 135985, 1587491, 13010537, 82162821, 424473531, 1868934548, ...

%e    ...

%Y Cf. A100754, A372067, A372068.

%K nonn,tabl

%O 1,5

%A _N. J. A. Sloane_, May 12 2024, based on emails from _Don Knuth_, May 06 2024 and May 08 2024