a(n) is the number of 132-avoiding permutations p so that p^3 is the identity permutation.

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =5a(5) =7a(6) =17a(7) =31a(8) =49a(9) =107a(10) =201a(11) =339a(12) =699a(13) =1327a(14) =2327a(15) =4643a(16) =8843a(17) =15895a(18) =31099a(19) =59251a(20) =108239a(21) =209239a(22) =398355a(23) =735619a(24) =1411351a(25) =2684147a(26) =4993111a(27) =9533775a(28) =18112735a(29) =33863375