cp's OEIS Frontend

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.

%I A372068 #19 May 15 2024 16:38:51
%S A372068 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,
%T A372068 1,64,272,506,506,272,64,1,1,128,688,1612,2103,1612,688,128,1,1,256,
%U A372068 1696,4856,7887,7887,4856,1696,256,1,1,512,4096,14016,27477,34088,27477,14016,4096,512,1
%N 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.
%C A372068 See the Knuth "Notes" link for much more information about these sequences. The present sequence is called "tab" in Part 2 of the Notes.
%H A372068 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
%e A372068 The initial antidiagonals are:
%e A372068    1,
%e A372068    1, 1,
%e A372068    1, 2, 1,
%e A372068    1, 4, 4, 1,
%e A372068    1, 8, 13, 8, 1,
%e A372068    1, 16, 38, 38, 16, 1,
%e A372068    1, 32, 104, 147, 104, 32, 1,
%e A372068    1, 64, 272, 506, 506, 272, 64, 1,
%e A372068    1, 128, 688, 1612, 2103, 1612, 688, 128, 1,
%e A372068    1, 256, 1696, 4856, 7887, 7887, 4856, 1696, 256, 1,
%e A372068    1, 512, 4096, 14016, 27477, 34088, 27477, 14016, 4096, 512, 1,
%e A372068    ...
%e A372068 The array begins:
%e A372068    1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A372068    1, 2, 4, 8, 16, 32, 64, 128, 256, 512, ...
%e A372068    1, 4, 13, 38, 104, 272, 688, 1696, 4096, 9728, ...
%e A372068    1, 8, 38, 147, 506, 1612, 4856, 14016, 39104, 106112, ...
%e A372068    1, 16, 104, 506, 2103, 7887, 27477, 90498, 285072, 865856, ...
%e A372068    1, 32, 272, 1612, 7887, 34088, 134825, 498465, 1746830, 5859404, ...
%e A372068    1, 64, 688, 4856, 27477, 134825, 597539, 2451038, 9455182, 34687916, ...
%e A372068    1, 128, 1696, 14016, 90498, 498465, 2451038, 11055950, 46570858, 185484836, ...
%e A372068    1, 256, 4096, 39104, 285072, 1746830, 9455182, 46570858, 212833803, 914854829, ...
%e A372068    1, 512, 9728, 106112, 865856, 5859404, 34687916, 185484836, 914854829, 4223468802, ...
%e A372068    ...
%Y A372068 Cf. A099594, A100754, A272644, A372066, A372067.
%K A372068 nonn,tabl
%O A372068 0,5
%A A372068 _N. J. A. Sloane_, May 12 2024, based on emails from _Don Knuth_, May 06 2024 and May 08 2024