"BIK" (reversible, indistinct, unlabeled) transform of 2,2,2,2...

Terms

a(0) =2a(1) =5a(2) =12a(3) =33a(4) =90a(5) =261a(6) =756a(7) =2241a(8) =6642a(9) =19845a(10) =59292a(11) =177633a(12) =532170a(13) =1595781a(14) =4785156a(15) =14353281a(16) =43053282a(17) =129153285a(18) =387440172a(19) =1162300833a(20) =3486843450a(21) =10460471301a(22) =31381236756a(23) =94143533121a(24) =282430067922a(25) =847289672325