a(0) = 1, a(1) = 2; for n>1, a(n) = a(n-1) + a(n-2) + floor(n/2).

Terms

a(0) =1a(1) =2a(2) =4a(3) =7a(4) =13a(5) =22a(6) =38a(7) =63a(8) =105a(9) =172a(10) =282a(11) =459a(12) =747a(13) =1212a(14) =1966a(15) =3185a(16) =5159a(17) =8352a(18) =13520a(19) =21881a(20) =35411a(21) =57302a(22) =92724a(23) =150037a(24) =242773a(25) =392822a(26) =635608a(27) =1028443a(28) =1664065a(29) =2692522