a(n) = a(n-1) + 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) =3a(4) =5a(5) =9a(6) =17a(7) =29a(8) =51a(9) =85a(10) =145a(11) =239a(12) =401a(13) =657a(14) =1087a(15) =1773a(16) =2911a(17) =4735a(18) =7731a(19) =12551a(20) =20427a(21) =33123a(22) =53789a(23) =87151a(24) =141341a(25) =228893a(26) =370891a(27) =600441a(28) =972419a(29) =1573947