a(2n) = A001542(n+1), a(2n+1) = A038761(n+1); a Pellian-related sequence.

Terms

a(0) =2a(1) =9a(2) =12a(3) =53a(4) =70a(5) =309a(6) =408a(7) =1801a(8) =2378a(9) =10497a(10) =13860a(11) =61181a(12) =80782a(13) =356589a(14) =470832a(15) =2078353a(16) =2744210a(17) =12113529a(18) =15994428a(19) =70602821a(20) =93222358a(21) =411503397a(22) =543339720a(23) =2398417561a(24) =3166815962a(25) =13979001969a(26) =18457556052a(27) =81475594253a(28) =107578520350a(29) =474874563549