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%I #23 Sep 09 2019 12:06:03
%S 0,0,0,0,0,0,0,1,0,0,0,2,1,0,0,0,5,3,1,0,0,0,7,9,5,2,0,0,0,12,16,15,6,
%T 2,0,0,0,16,29,29,22,9,2,0,0,0,22,43,59,52,32,12,3,0,0,0,28,64,103,
%U 112,82,40,15,3,0,0,0,37,92,168,212,199,122,59,17,3,0,0,0,43,127,259,376,407
%N Rectangular array T(n,k) = number of nondecreasing sequences of n 1..k integers with no element dividing the sequence sum (for n, k >= 1), read by decreasing antidiagonals.
%C Table starts:
%C 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
%C 0 0 1 2 5 7 12 16 22 28 37 43 54 64 75 86 ...
%C 0 0 1 3 9 16 29 43 64 92 127 168 219 281 355 435 ...
%C 0 0 1 5 15 29 59 103 168 259 386 553 772 1043 1401 1832 ...
%C 0 0 2 6 22 52 112 212 376 640 1011 1560 2293 3328 4711 6524 ...
%C 0 0 2 9 32 82 199 407 796 1424 2407 3948 6166 9456 14171 20556 ...
%C 0 0 2 12 40 122 319 722 1503 2872 5159 9087 15030 24441 38349 58701 ...
%C 0 0 3 15 59 182 503 1214 2693 5517 10574 19715 34318 58653 96517 154975 ...
%C 0 0 3 17 74 259 733 1912 4560 10052 20363 39988 73196 131054 225666 378925 ...
%C 0 0 3 22 97 363 1067 2960 7533 17497 37344 77105 148113 276174 498304 873878 ...
%C ...
%H R. H. Hardin, <a href="/A212868/b212868.txt">Table of n, a(n) for n = 1..958</a>
%e All solutions for n=8 and k=4:
%e 2 2 2 3 3 2 2 2 2 3 2 2 2 3 2
%e 2 3 2 4 3 2 2 2 2 3 2 2 3 3 3
%e 2 3 3 4 3 2 3 2 2 3 2 2 3 3 4
%e 2 3 3 4 4 2 3 3 2 3 3 2 3 3 4
%e 2 3 3 4 4 2 3 3 2 3 4 3 3 3 4
%e 3 3 4 4 4 2 3 3 2 3 4 4 3 3 4
%e 3 3 4 4 4 2 3 4 3 4 4 4 4 3 4
%e 3 3 4 4 4 3 4 4 4 4 4 4 4 4 4
%Y Cf. A161664 (row 2, cicada cycles), A212870 (row 3), A212871 (row 4), A212872 (row 5), A212873 (row 6), A212874 (row 7).
%Y Cf. A212864 (column 4), A212865 (column 5), A212866 (column 6), A212867 (column 7).
%Y Cf. A212869 (superdiagonal 1).
%K nonn,tabl
%O 1,12
%A _R. H. Hardin_, May 29 2012
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