This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A320796 Regular triangle where T(n,k) is the number of non-isomorphic self-dual multiset partitions of weight n with k parts. 17
 1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 5, 7, 3, 1, 1, 7, 14, 10, 3, 1, 1, 9, 23, 24, 11, 3, 1, 1, 12, 39, 53, 34, 12, 3, 1, 1, 14, 61, 102, 86, 39, 12, 3, 1, 1, 17, 90, 193, 201, 117, 42, 12, 3, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Also the number of nonnegative integer k X k symmetric matrices with sum of elements equal to n and no zero rows or columns, up to row and column permutations. The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}. The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices. LINKS EXAMPLE Triangle begins:    1    1   1    1   2   1    1   4   3   1    1   5   7   3   1    1   7  14  10   3   1    1   9  23  24  11   3   1    1  12  39  53  34  12   3   1    1  14  61 102  86  39  12   3   1    1  17  90 193 201 117  42  12   3   1 Non-isomorphic representatives of the multiset partitions for n = 1 through 5 (commas elided): 1: {{1}} . 2: {{11}}  {{1}{2}} . 3: {{111}}  {{1}{22}}  {{1}{2}{3}} .           {{2}{12}} . 4: {{1111}}  {{11}{22}}  {{1}{1}{23}}  {{1}{2}{3}{4}} .            {{12}{12}}  {{1}{2}{33}} .            {{1}{222}}  {{1}{3}{23}} .            {{2}{122}} . 5: {{11111}}  {{11}{122}}  {{1}{22}{33}}  {{1}{2}{2}{34}}  {{1}{2}{3}{4}{5}} .             {{11}{222}}  {{1}{23}{23}}  {{1}{2}{3}{44}} .             {{12}{122}}  {{1}{2}{333}}  {{1}{2}{4}{34}} .             {{1}{2222}}  {{1}{3}{233}} .             {{2}{1222}}  {{2}{12}{33}} .                          {{2}{13}{23}} .                          {{3}{3}{123}} CROSSREFS Row sums are A316983. Cf. A000219, A007716, A316980, A317533, A318805, A319560, A319616, A319721, A320797-A320813. Sequence in context: A112096 A217874 A229118 * A026725 A026758 A130523 Adjacent sequences:  A320793 A320794 A320795 * A320797 A320798 A320799 KEYWORD nonn,tabl AUTHOR Gus Wiseman, Nov 02 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 17 09:43 EST 2018. Contains 318193 sequences. (Running on oeis4.)