Sequences A001644 and A000073 interleaved.

Terms

a(0) =3a(1) =1a(2) =3a(3) =2a(4) =11a(5) =7a(6) =39a(7) =24a(8) =131a(9) =81a(10) =443a(11) =274a(12) =1499a(13) =927a(14) =5071a(15) =3136a(16) =17155a(17) =10609a(18) =58035a(19) =35890a(20) =196331a(21) =121415a(22) =664183a(23) =410744a(24) =2246915a(25) =1389537a(26) =7601259a(27) =4700770a(28) =25714875a(29) =15902591