a(n) is the number of cyclic permutations that admit a [1,1,-1]-gridding.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =5a(5) =15a(6) =42a(7) =120a(8) =338a(9) =952a(10) =2671a(11) =7494a(12) =21035a(13) =59115a(14) =166432a(15) =469560a(16) =1327802a(17) =3763545a(18) =10692500a(19) =30447858a(20) =86894361a(21) =248506757a(22) =712109662a(23) =2044402512a(24) =5879579540a(25) =16937048040a(26) =48864612667a(27) =141179970820a(28) =408444645375