A323949 Number of set partitions of {1, ..., n} with no block containing three distinct cyclically successive vertices.

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

Alois P. Heinz, Table of n, a(n) for n = 0..250

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}]

Crossrefs

Cf. A000085, A000110, A000126, A000296, A000325, A001610, A001644, A078012, A169985.

Cf. A306351, A306357, A323950, A323951, A323953, A323954, A323955, A323956.

Sequence in context: A006396 A192502 A243567 * A066278 A210773 A210774

Adjacent sequences: A323946 A323947 A323948 * A323950 A323951 A323952

Keyword

nonn

Author

Gus Wiseman, Feb 10 2019

Extensions

a(12)-a(25) from Alois P. Heinz, Feb 10 2019

Status

approved