A006005 (shifted) convolved with all of its regularly "aerated" variants.

Terms

a(0) =1a(1) =3a(2) =8a(3) =19a(4) =43a(5) =85a(6) =171a(7) =315a(8) =580a(9) =1022a(10) =1766a(11) =2982a(12) =4959a(13) =8081a(14) =12997a(15) =20596a(16) =32261a(17) =49909a(18) =76447a(19) =115872a(20) =174133a(21) =259312a(22) =383206a(23) =561877a(24) =818225a(25) =1183266a(26) =1700658a(27) =2429266a(28) =3450562a(29) =4874167