a(n) = a(n-1) + floor((a(n-2) + a(n-3))/2), with a(n)=1 for n < 3.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =4a(6) =6a(7) =9a(8) =14a(9) =21a(10) =32a(11) =49a(12) =75a(13) =115a(14) =177a(15) =272a(16) =418a(17) =642a(18) =987a(19) =1517a(20) =2331a(21) =3583a(22) =5507a(23) =8464a(24) =13009a(25) =19994a(26) =30730a(27) =47231a(28) =72593a(29) =111573