G.f. := (1-sqrt(1-4*x+4*x^2-4*x^3))/(2(1-x+x^2)x).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =5a(5) =12a(6) =29a(7) =73a(8) =190a(9) =505a(10) =1363a(11) =3727a(12) =10306a(13) =28771a(14) =80975a(15) =229512a(16) =654545a(17) =1876899a(18) =5408142a(19) =15650939a(20) =45470545a(21) =132573406a(22) =387775229a(23) =1137575084a(24) =3346189045a(25) =9867291817a(26) =29163523978a(27) =86377998093a(28) =256343194011