a(n) = a(n-3) + a(n-2) + gcd(a(n-2), a(n-1)) with a(1) = a(2) = a(3) = 1.

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =3a(5) =7a(6) =7a(7) =17a(8) =15a(9) =25a(10) =37a(11) =41a(12) =63a(13) =79a(14) =105a(15) =143a(16) =185a(17) =249a(18) =329a(19) =435a(20) =579a(21) =767a(22) =1015a(23) =1347a(24) =1783a(25) =2363a(26) =3131a(27) =4147a(28) =5495a(29) =7279