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

Terms

a(0) =0a(1) =1a(2) =3a(3) =6a(4) =12a(5) =21a(6) =37a(7) =62a(8) =104a(9) =171a(10) =281a(11) =458a(12) =746a(13) =1211a(14) =1965a(15) =3184a(16) =5158a(17) =8351a(18) =13519a(19) =21880a(20) =35410a(21) =57301a(22) =92723a(23) =150036a(24) =242772a(25) =392821a(26) =635607a(27) =1028442a(28) =1664064a(29) =2692521