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%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
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