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A323949
Number of set partitions of {1, ..., n} with no block containing three distinct cyclically successive vertices.
3
1, 1, 2, 4, 10, 36, 145, 631, 3015, 15563, 86144, 508311, 3180930, 21018999, 146111543, 1065040886, 8117566366, 64531949885, 533880211566, 4587373155544, 40865048111424, 376788283806743, 3590485953393739, 35312436594162173, 357995171351223109, 3736806713651177702
OFFSET
0,3
COMMENTS
Cyclically successive means 1 is a successor of n.
LINKS
EXAMPLE
The a(1) = 1 through a(4) = 10 set partitions:
{{1}} {{1,2}} {{1},{2,3}} {{1,2},{3,4}}
{{1},{2}} {{1,2},{3}} {{1,3},{2,4}}
{{1,3},{2}} {{1,4},{2,3}}
{{1},{2},{3}} {{1},{2},{3,4}}
{{1},{2,3},{4}}
{{1,2},{3},{4}}
{{1},{2,4},{3}}
{{1,3},{2},{4}}
{{1,4},{2},{3}}
{{1},{2},{3},{4}}
MATHEMATICA
spsu[_, {}]:={{}}; spsu[foo_, set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@spsu[Select[foo, Complement[#, Complement[set, s]]=={}&], Complement[set, s]]]/@Cases[foo, {i, ___}];
Table[Length[spsu[Select[Subsets[Range[n]], Select[Partition[Range[n], 3, 1, 1], Function[ed, UnsameQ@@ed&&Complement[ed, #]=={}]]=={}&], Range[n]]], {n, 8}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 10 2019
EXTENSIONS
a(12)-a(25) from Alois P. Heinz, Feb 10 2019
STATUS
approved