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A068598
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Number of maximal sets of partitions of n with property that all parts in all partitions in the set are distinct.
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0
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1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 6, 8, 13, 18, 31, 47, 75, 115, 199, 312, 533, 888, 1536, 2535, 4608, 7694
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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COMMENTS
| Also number of cliques in following graph: each distinct partition of n represents a vertex, the relation "having no common integer" defines the edges connecting these. - Wouter Meeussen (wouter.meeussen(AT)pandora.be), May 27 2002
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LINKS
| Naohiro Nomoto, a(0)-a(13) [Broken link?]
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EXAMPLE
| a(8) = 3: {8=1+7=2+6=3+5, 8=1+2+5, 8=1+3+4=2+6}.
a(11) = 8: {11=1+10=2+9=3+8=4+7=5+6, 11=1+2+8=4+7=5+6, 11=1+3+7=2+9=5+6, 11=1+4+6=3+8=2+9, 11=2+3+6=4+7=1+10, 11=2+4+5=1+10=3+8, 11=1+2+3+5=4+7, 11=2+4+5=1+3+7}.
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MATHEMATICA
| maximal[hit_List, candi_List] := Not[Or@@(UnsameQ@@Flatten[{candi, #}]&/@hit)]; (* write 'ListQPartitions[n]' to list all distinct partitions of n *) Table[it=ListQPartitions[n]; Length@DeleteCases[Backtrack[{#, {}}&/@it, UnsameQ@@Flatten[{#}]&, maximal[it, DeleteCases[ #, {}]]&, All], {}, -1], {n, 3, 14}]
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CROSSREFS
| Cf. A000009.
Sequence in context: A006207 A017912 A102543 * A163770 A035561 A068106
Adjacent sequences: A068595 A068596 A068597 * A068599 A068600 A068601
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KEYWORD
| hard,nonn,nice
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AUTHOR
| Naohiro Nomoto (n_nomoto(AT)yabumi.com), Mar 28 2002
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EXTENSIONS
| More terms from Wouter Meeussen (wouter.meeussen(AT)pandora.be), May 27 2002
a(25) from Robert G. Wilson v (rgwv(AT)rgwv.com), May 29 2002
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