a(n) = a(n-1) + 2*a(n-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) =16a(6) =34a(7) =70a(8) =145a(9) =292a(10) =598a(11) =1198a(12) =2428a(13) =4858a(14) =9784a(15) =19570a(16) =39283a(17) =78568a(18) =157426a(19) =314854a(20) =630304a(21) =1260610a(22) =2522416a(23) =5044834a(24) =10092094a(25) =20184190a(26) =40373236a(27) =80746474a(28) =161502730a(29) =323005462