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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =2a(5) =3a(6) =3a(7) =4a(8) =5a(9) =6a(10) =7a(11) =9a(12) =11a(13) =13a(14) =16a(15) =20a(16) =24a(17) =29a(18) =35a(19) =43a(20) =52a(21) =62a(22) =75a(23) =91a(24) =110a(25) =133a(26) =161a(27) =194a(28) =234a(29) =283