Number of n-bead necklaces labeled with numbers -1..1 not allowing reversal, with sum zero.

Terms

a(0) =1a(1) =2a(2) =3a(3) =6a(4) =11a(5) =26a(6) =57a(7) =142a(8) =351a(9) =902a(10) =2333a(11) =6166a(12) =16381a(13) =44046a(14) =119183a(15) =324862a(16) =890291a(17) =2453126a(18) =6789309a(19) =18869426a(20) =52635789a(21) =147325510a(22) =413618615a(23) =1164517198a(24) =3287073461a(25) =9300516890a(26) =26372968983a(27) =74937177538a(28) =213333642443a(29) =608400919106