a(n) = b_f(n) where f is the 3-periodic sequence [-1,1,5] (see comments).

Terms

a(0) =2a(1) =11a(2) =19a(3) =41a(4) =71a(5) =107a(6) =191a(7) =301a(8) =431a(9) =565a(10) =857a(11) =1133a(12) =1325a(13) =2657a(14) =5231a(15) =10457a(16) =19421a(17) =29567a(18) =54497a(19) =105527a(20) =211061a(21) =408431a(22) =802127a(23) =1600217a(24) =3200201a(25) =6393911a(26) =12783497a(27) =25566677a(28) =51095411a(29) =102190391