OFFSET
1,3
COMMENTS
Cyclically successive means 1 is a successor of n.
EXAMPLE
Triangle begins:
1
1 2
1 4 5
4 10 14 15
11 36 46 51 52
41 145 184 196 202 203
162 631 806 855 869 876 877
715 3015 3847 4059 4115 4131 4139 4140
Row 4 counts the following partitions:
{{13}{24}} {{12}{34}} {{1}{234}} {{1234}}
{{1}{24}{3}} {{13}{24}} {{12}{34}} {{1}{234}}
{{13}{2}{4}} {{14}{23}} {{123}{4}} {{12}{34}}
{{1}{2}{3}{4}} {{1}{2}{34}} {{124}{3}} {{123}{4}}
{{1}{23}{4}} {{13}{24}} {{124}{3}}
{{12}{3}{4}} {{134}{2}} {{13}{24}}
{{1}{24}{3}} {{14}{23}} {{134}{2}}
{{13}{2}{4}} {{1}{2}{34}} {{14}{23}}
{{14}{2}{3}} {{1}{23}{4}} {{1}{2}{34}}
{{1}{2}{3}{4}} {{12}{3}{4}} {{1}{23}{4}}
{{1}{24}{3}} {{12}{3}{4}}
{{13}{2}{4}} {{1}{24}{3}}
{{14}{2}{3}} {{13}{2}{4}}
{{1}{2}{3}{4}} {{14}{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], k, 1, 1], Function[ed, UnsameQ@@ed&&Complement[ed, #]=={}]]=={}&], Range[n]]], {n, 7}, {k, 2, n+1}]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Feb 10 2019
STATUS
approved