A082185 Triangle read by rows: n-th row contains concatenations of nonempty subsets of {1, 2, ..., n}, ordered first by size and then lexicographically.

1, 1, 2, 12, 1, 2, 3, 12, 13, 23, 123, 1, 2, 3, 4, 12, 13, 14, 23, 24, 34, 123, 124, 134, 234, 1234, 1, 2, 3, 4, 5, 12, 13, 14, 15, 23, 24, 25, 34, 35, 45, 123, 124, 125, 134, 135, 145, 234, 235, 245, 345, 1234, 1235, 1245, 1345, 2345, 12345, 1, 2, 3, 4, 5, 6, 12, 13, 14, 15

Offset: 1

Author

M. Khoshnevisan (m.khoshnevisan(AT)griffith.edu.au), May 10 2003

Keywords

• nonn
• easy
• tabf
• base

Examples

			Triangle T(n,k) begins:
  1;
  1, 2, 12;
  1, 2,  3, 12, 13, 23, 123;
  1, 2,  3,  4, 12, 13,  14, 23, 24, 34, 123, 124, 134, 234, 1234;
  ...
		

References

• F. Smarandache and J. Dezert, Advances and Applications of DSmT for Information Fusion, Vol. 1, ARPress, 2004, pp. 42-46.

Links

• Alois P. Heinz, Rows n = 1..9, flattened
• J. Dezert and F. Smarandache On the generation of hyper-powersets for the DSmT, Proc. Fusion 2003 Conf., Cairns, Australia.
• F. Smarandache and J. Dezert, Advances and Applications of DSmT for Information Fusion, Vol. 1, 2004.
• Florentin Smarandache, Algebraic Generalization of Venn Diagram, in Multispace & Multistructure. Neutrosophic Transdisciplinarity, NESP, 2010.

Programs

Maple

T:= n-> map(x-> parse(cat(x[])),
       [seq(combinat[choose]([$1..n], i)[], i=1..n)])[]:
seq(T(n), n=1..6);  # Alois P. Heinz, Jan 30 2023

Extensions

More terms from David Wasserman, Aug 19 2004