a(n) = floor( e^((n/2)*arccosh(1+sqrt(2))) ).

Terms

a(0) =1a(1) =2a(2) =4a(3) =9a(4) =21a(5) =45a(6) =98a(7) =210a(8) =452a(9) =971a(10) =2085a(11) =4478a(12) =9618a(13) =20654a(14) =44355a(15) =95252a(16) =204549a(17) =439262a(18) =943298a(19) =2025695a(20) =4350099a(21) =9341661a(22) =20060837a(23) =43079834a(24) =92512195a(25) =198666181a(26) =426627554a(27) =916165344a(28) =1967427861a(29) =4224971416