a(n) = Sum_{k >= 1} floor((1+sqrt(2))^(n-k)).

Terms

a(0) =1a(1) =3a(2) =8a(3) =22a(4) =55a(5) =137a(6) =334a(7) =812a(8) =1965a(9) =4751a(10) =11476a(11) =27714a(12) =66915a(13) =161557a(14) =390042a(15) =941656a(16) =2273369a(17) =5488411a(18) =13250208a(19) =31988846a(20) =77227919a(21) =186444705a(22) =450117350a(23) =1086679428a(24) =2623476229a(25) =6333631911a(26) =15290740076