Subsequence of A005428 where state = 2.

Terms

a(0) =1a(1) =2a(2) =3a(3) =14a(4) =21a(5) =47a(6) =158a(7) =237a(8) =533a(9) =1199a(10) =4046a(11) =6069a(12) =13655a(13) =46085a(14) =103691a(15) =1181102a(16) =1771653a(17) =3986219a(18) =102162425a(19) =229865456a(20) =344798184a(21) =517197276a(22) =775795914a(23) =1163693871a(24) =3927466814a(25) =5891200221a(26) =13255200497a(27) =29824201118a(28) =44736301677a(29) =100656678773