a(n) = a(n-1) + a(n-2) + 2 a([(n-1)/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) =22a(7) =43a(8) =73a(9) =130a(10) =217a(11) =373a(12) =616a(13) =1033a(14) =1693a(15) =2812a(16) =4591a(17) =7549a(18) =12286a(19) =20095a(20) =32641a(21) =53170a(22) =86245a(23) =140161a(24) =227152a(25) =368545a(26) =596929a(27) =967540a(28) =1566535a(29) =2537461