A325766 Number of integer partitions of n covering an initial interval of positive integers and containing their own multiset of multiplicities (as a submultiset).
1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 1, 5, 4, 5, 4, 6, 7, 8, 6, 12, 11, 19, 16, 22, 22, 25, 32, 38, 45, 45, 51, 53, 71, 69, 85, 92, 118, 125, 147, 149, 184, 187, 230, 254, 290, 317, 372, 397, 449, 502, 544, 616, 680, 758, 841, 930, 1042, 1151, 1262
Offset: 0
Keywords
Examples
The initial terms count the following partitions: 1: (1) 4: (2,1,1) 5: (2,2,1) 6: (2,2,1,1) 7: (3,2,1,1) 8: (3,2,1,1,1) 9: (3,2,2,1,1) 10: (3,2,2,1,1,1) 11: (3,3,2,2,1) 11: (3,3,2,1,1,1) 11: (3,2,2,2,1,1) 12: (4,3,2,1,1,1) 13: (4,3,2,2,1,1) 13: (4,3,2,1,1,1,1) 13: (3,3,3,2,1,1) 13: (3,3,2,2,2,1) 13: (3,3,2,2,1,1,1) 14: (4,3,2,2,1,1,1) 14: (3,3,3,2,2,1) 14: (3,3,3,2,1,1,1) 14: (3,3,2,2,2,1,1)
Crossrefs
Programs
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Mathematica
submultQ[cap_,fat_]:=And@@Function[i,Count[fat,i]>=Count[cap,i]]/@Union[List@@cap] Table[Length[Select[IntegerPartitions[n],Range[Length[Union[#]]]==Union[#]&&submultQ[Sort[Length/@Split[#]],Sort[#]]&]],{n,0,30}]
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