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

1,3

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

Jean Dezert and Florentin Smarandache, On the generation of hyper-powersets for the DSmT, Proc. Fusion 2003 Conf., Cairns, Australia.

Florentin Smarandache and Jean 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.

Example

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;
  ...

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

Crossrefs

Sequence in context: A016736 A287704 A351456 * A354130 A113491 A107773

Adjacent sequences: A082182 A082183 A082184 * A082186 A082187 A082188

Keyword

nonn,easy,tabf,base

Author

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

Extensions

More terms from David Wasserman, Aug 19 2004

Status

approved