"BGK" (reversible, element, unlabeled) transform of 2,2,2,2,...

Terms

a(0) =1a(1) =2a(2) =3a(3) =6a(4) =13a(5) =22a(6) =53a(7) =104a(8) =189a(9) =420a(10) =739a(11) =1420a(12) =2687a(13) =5198a(14) =8907a(15) =15762a(16) =30709a(17) =51322a(18) =92765a(19) =153932a(20) =275181a(21) =478560a(22) =806515a(23) =1334656a(24) =2222951a(25) =3864914a(26) =6233763a(27) =10538622a(28) =16896061a(29) =27407110