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

Terms

a(0) =1a(1) =-1a(2) =4a(3) =-10a(4) =23a(5) =-59a(6) =138a(7) =-340a(8) =813a(9) =-1973a(10) =4752a(11) =-11486a(12) =27715a(13) =-66927a(14) =161558a(15) =-390056a(16) =941657a(17) =-2273385a(18) =5488412a(19) =-13250226a(20) =31988847a(21) =-77227939a(22) =186444706a(23) =-450117372a(24) =1086679429a(25) =-2623476253a(26) =6333631912a(27) =-15290740102a(28) =36915112091a(29) =-89120964311