From a riddle, see Puzzling.SE link.

Terms

a(0) =3a(1) =1a(2) =4a(3) =8a(4) =8a(5) =21a(6) =21a(7) =62a(8) =128a(9) =190a(10) =430a(11) =831a(12) =1451a(13) =3030a(14) =6143a(15) =12286a(16) =24361a(17) =48850a(18) =85497a(19) =134347a(20) =268694a(21) =583208a(22) =1071746a(23) =2192342a(24) =3264088a(25) =7514425a(26) =14042601a(27) =24821114a(28) =46378140a(29) =99867664