A212868 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.

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

Offset: 1

Author

R. H. Hardin, May 29 2012

Keywords

• nonn
• tabl

Comments

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 ...

...

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..958

Crossrefs

Cf. A161664 (row 2, cicada cycles), A212870 (row 3), A212871 (row 4), A212872 (row 5), A212873 (row 6), A212874 (row 7).

Cf. A212864 (column 4), A212865 (column 5), A212866 (column 6), A212867 (column 7).

Cf. A212869 (superdiagonal 1).