a(n) = round(n^3/12) - floor(n/4)*floor((n+2)/4).

Terms

a(0) =0a(1) =0a(2) =1a(3) =2a(4) =4a(5) =9a(6) =16a(7) =27a(8) =39a(9) =57a(10) =77a(11) =105a(12) =135a(13) =174a(14) =217a(15) =269a(16) =325a(17) =393a(18) =466a(19) =552a(20) =642a(21) =747a(22) =857a(23) =984a(24) =1116a(25) =1266a(26) =1423a(27) =1598a(28) =1780a(29) =1983