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A212868
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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.
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11
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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, 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, 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
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OFFSET
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1,12
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COMMENTS
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Table starts:
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
0 0 1 2 5 7 12 16 22 28 37 43 54 64 75 86 ...
0 0 1 3 9 16 29 43 64 92 127 168 219 281 355 435 ...
0 0 1 5 15 29 59 103 168 259 386 553 772 1043 1401 1832 ...
0 0 2 6 22 52 112 212 376 640 1011 1560 2293 3328 4711 6524 ...
0 0 2 9 32 82 199 407 796 1424 2407 3948 6166 9456 14171 20556 ...
0 0 2 12 40 122 319 722 1503 2872 5159 9087 15030 24441 38349 58701 ...
0 0 3 15 59 182 503 1214 2693 5517 10574 19715 34318 58653 96517 154975 ...
0 0 3 17 74 259 733 1912 4560 10052 20363 39988 73196 131054 225666 378925 ...
0 0 3 22 97 363 1067 2960 7533 17497 37344 77105 148113 276174 498304 873878 ...
...
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LINKS
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EXAMPLE
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All solutions for n=8 and k=4:
2 2 2 3 3 2 2 2 2 3 2 2 2 3 2
2 3 2 4 3 2 2 2 2 3 2 2 3 3 3
2 3 3 4 3 2 3 2 2 3 2 2 3 3 4
2 3 3 4 4 2 3 3 2 3 3 2 3 3 4
2 3 3 4 4 2 3 3 2 3 4 3 3 3 4
3 3 4 4 4 2 3 3 2 3 4 4 3 3 4
3 3 4 4 4 2 3 4 3 4 4 4 4 3 4
3 3 4 4 4 3 4 4 4 4 4 4 4 4 4
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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