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A321143 Number of non-isomorphic knapsack multiset partitions of weight n. 2
1, 1, 4, 10, 31, 87, 272, 835, 2673, 8805, 29583 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A multiset partition is knapsack if every distinct submultiset of the parts has a different multiset union.

LINKS

Table of n, a(n) for n=0..10.

EXAMPLE

Non-isomorphic representatives of the a(1) = 1 through a(4) = 31 knapsack multiset partitions:

  {{1}}  {{1,1}}    {{1,1,1}}      {{1,1,1,1}}

         {{1,2}}    {{1,2,2}}      {{1,1,2,2}}

         {{1},{1}}  {{1,2,3}}      {{1,2,2,2}}

         {{1},{2}}  {{1},{1,1}}    {{1,2,3,3}}

                    {{1},{2,2}}    {{1,2,3,4}}

                    {{1},{2,3}}    {{1},{1,1,1}}

                    {{2},{1,2}}    {{1,1},{1,1}}

                    {{1},{1},{1}}  {{1},{1,2,2}}

                    {{1},{2},{2}}  {{1,1},{2,2}}

                    {{1},{2},{3}}  {{1,2},{1,2}}

                                   {{1},{2,2,2}}

                                   {{1,2},{2,2}}

                                   {{1},{2,3,3}}

                                   {{1,2},{3,3}}

                                   {{1},{2,3,4}}

                                   {{1,2},{3,4}}

                                   {{1,3},{2,3}}

                                   {{2},{1,2,2}}

                                   {{3},{1,2,3}}

                                   {{1},{1},{2,2}}

                                   {{1},{1},{2,3}}

                                   {{1},{2},{2,2}}

                                   {{1},{2},{3,3}}

                                   {{1},{2},{3,4}}

                                   {{1},{3},{2,3}}

                                   {{2},{2},{1,2}}

                                   {{1},{1},{1},{1}}

                                   {{1},{1},{2},{2}}

                                   {{1},{2},{2},{2}}

                                   {{1},{2},{3},{3}}

                                   {{1},{2},{3},{4}}

Missing from this list are {{1},{1},{1,1}} and {{1},{2},{1,2}}, which are not knapsack.

CROSSREFS

Cf.  A002219, A006827, A007716, A108917, A275972, A276024, A292886, A316983, A319616.

Sequence in context: A264564 A304963 A034730 * A095127 A006342 A258041

Adjacent sequences:  A321140 A321141 A321142 * A321144 A321145 A321146

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Oct 28 2018

STATUS

approved

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Last modified May 29 20:42 EDT 2020. Contains 334710 sequences. (Running on oeis4.)