a(2n) = A100525(n), a(2n+1) = A001653(n+1); a Pellian-related sequence.

Terms

a(0) =4a(1) =5a(2) =22a(3) =29a(4) =128a(5) =169a(6) =746a(7) =985a(8) =4348a(9) =5741a(10) =25342a(11) =33461a(12) =147704a(13) =195025a(14) =860882a(15) =1136689a(16) =5017588a(17) =6625109a(18) =29244646a(19) =38613965a(20) =170450288a(21) =225058681a(22) =993457082a(23) =1311738121a(24) =5790292204a(25) =7645370045a(26) =33748296142a(27) =44560482149a(28) =196699484648a(29) =259717522849