a(n) = floor((1+sqrt(2))^n).

Terms

a(0) =1a(1) =2a(2) =5a(3) =14a(4) =33a(5) =82a(6) =197a(7) =478a(8) =1153a(9) =2786a(10) =6725a(11) =16238a(12) =39201a(13) =94642a(14) =228485a(15) =551614a(16) =1331713a(17) =3215042a(18) =7761797a(19) =18738638a(20) =45239073a(21) =109216786a(22) =263672645a(23) =636562078a(24) =1536796801a(25) =3710155682a(26) =8957108165a(27) =21624372014a(28) =52205852193