a(n) = a(n-1) + a(n-2) + 2 a([n/2]), where a(0) = 1, a(1) = 1, a(2) = 1.

Terms

a(0) =1a(1) =1a(2) =1a(3) =4a(4) =7a(5) =13a(6) =28a(7) =49a(8) =91a(9) =154a(10) =271a(11) =451a(12) =778a(13) =1285a(14) =2161a(15) =3544a(16) =5887a(17) =9613a(18) =15808a(19) =25729a(20) =42079a(21) =68350a(22) =111331a(23) =180583a(24) =293470a(25) =475609a(26) =771649a(27) =1249828a(28) =2025799a(29) =3279949