Number of polygonal cacti (Husimi graphs) with n nodes.

Terms

a(0) =1a(1) =1a(2) =0a(3) =1a(4) =1a(5) =2a(6) =2a(7) =5a(8) =7a(9) =16a(10) =28a(11) =63a(12) =131a(13) =301a(14) =673a(15) =1600a(16) =3773a(17) =9158a(18) =22319a(19) =55255a(20) =137563a(21) =345930a(22) =874736a(23) =2227371a(24) =5700069a(25) =14664077a(26) =37888336a(27) =98310195a(28) =256037795a(29) =669184336