a(n) = Sum_{k=0..n} ceiling((1 + sqrt(2))^k).

Terms

a(0) =1a(1) =4a(2) =10a(3) =25a(4) =59a(5) =142a(6) =340a(7) =819a(8) =1973a(9) =4760a(10) =11486a(11) =27725a(12) =66927a(13) =161570a(14) =390056a(15) =941671a(16) =2273385a(17) =5488428a(18) =13250226a(19) =31988865a(20) =77227939a(21) =186444726a(22) =450117372a(23) =1086679451a(24) =2623476253a(25) =6333631936a(26) =15290740102a(27) =36915112117a(28) =89120964311a(29) =215157040714