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A082185 Triangle read by rows: n-th row contains concatenations of nonempty subsets of {1, 2, ..., n}, ordered first by size and then lexicographically. 6

%I #19 Jan 30 2023 10:53:54

%S 1,1,2,12,1,2,3,12,13,23,123,1,2,3,4,12,13,14,23,24,34,123,124,134,

%T 234,1234,1,2,3,4,5,12,13,14,15,23,24,25,34,35,45,123,124,125,134,135,

%U 145,234,235,245,345,1234,1235,1245,1345,2345,12345,1,2,3,4,5,6,12,13,14,15

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

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

%H Alois P. Heinz, <a href="/A082185/b082185.txt">Rows n = 1..9, flattened</a>

%H J. Dezert and F. Smarandache <a href="http://www.gallup.unm.edu/~smarandache/hyper-powerset.pdf">On the generation of hyper-powersets for the DSmT</a>, Proc. Fusion 2003 Conf., Cairns, Australia.

%H F. Smarandache and J. Dezert, <a href="http://www.gallup.unm.edu/~smarandache/DSmT-book1">Advances and Applications of DSmT for Information Fusion, Vol. 1, 2004</a>.

%H Florentin Smarandache, <a href="http://hal-ensieta.archives-ouvertes.fr/docs/00/48/84/87/PDF/Generalization_of_Venn_Diagram-ensieta.pdf">Algebraic Generalization of Venn Diagram</a>, in Multispace & Multistructure. Neutrosophic Transdisciplinarity, NESP, 2010.

%e Triangle T(n,k) begins:

%e 1;

%e 1, 2, 12;

%e 1, 2, 3, 12, 13, 23, 123;

%e 1, 2, 3, 4, 12, 13, 14, 23, 24, 34, 123, 124, 134, 234, 1234;

%e ...

%p T:= n-> map(x-> parse(cat(x[])),

%p [seq(combinat[choose]([$1..n], i)[], i=1..n)])[]:

%p seq(T(n), n=1..6); # _Alois P. Heinz_, Jan 30 2023

%K nonn,easy,tabf,base

%O 1,3

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

%E More terms from _David Wasserman_, Aug 19 2004

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Last modified March 28 14:33 EDT 2024. Contains 371254 sequences. (Running on oeis4.)