A323949 - OEIS

%I #16 Feb 10 2019 19:01:20

%S 1,1,2,4,10,36,145,631,3015,15563,86144,508311,3180930,21018999,

%T 146111543,1065040886,8117566366,64531949885,533880211566,

%U 4587373155544,40865048111424,376788283806743,3590485953393739,35312436594162173,357995171351223109,3736806713651177702

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

%C Cyclically successive means 1 is a successor of n.

%H Alois P. Heinz, <a href="/A323949/b323949.txt">Table of n, a(n) for n = 0..250</a>

%e The a(1) = 1 through a(4) = 10 set partitions:

%e   {{1}}  {{1,2}}    {{1},{2,3}}    {{1,2},{3,4}}

%e          {{1},{2}}  {{1,2},{3}}    {{1,3},{2,4}}

%e                     {{1,3},{2}}    {{1,4},{2,3}}

%e                     {{1},{2},{3}}  {{1},{2},{3,4}}

%e                                    {{1},{2,3},{4}}

%e                                    {{1,2},{3},{4}}

%e                                    {{1},{2,4},{3}}

%e                                    {{1,3},{2},{4}}

%e                                    {{1,4},{2},{3}}

%e                                    {{1},{2},{3},{4}}

%t spsu[_,{}]:={{}};spsu[foo_,set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@spsu[Select[foo,Complement[#,Complement[set,s]]=={}&],Complement[set,s]]]/@Cases[foo,{i,___}];

%t Table[Length[spsu[Select[Subsets[Range[n]],Select[Partition[Range[n],3,1,1],Function[ed,UnsameQ@@ed&&Complement[ed,#]=={}]]=={}&],Range[n]]],{n,8}]

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

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

%K nonn

%O 0,3

%A _Gus Wiseman_, Feb 10 2019

%E a(12)-a(25) from _Alois P. Heinz_, Feb 10 2019