A035539 with periodic zeros stripped.

Terms

a(0) =1a(1) =4a(2) =11a(3) =27a(4) =59a(5) =123a(6) =241a(7) =458a(8) =838a(9) =1498a(10) =2608a(11) =4459a(12) =7473a(13) =12339a(14) =20058a(15) =32197a(16) =51027a(17) =80003a(18) =124092a(19) =190683a(20) =290322a(21) =438392a(22) =656681a(23) =976479a(24) =1441726a(25) =2114700a(26) =3082164a(27) =4465650a(28) =6433177a(29) =9217720