a(n) = Sum_{-n<i<n, -n<j<n, gcd{i,j}=2} (n-|i|)*(n-|j|)/8.

Terms

a(0) =0a(1) =0a(2) =2a(3) =6a(4) =15a(5) =28a(6) =53a(7) =86a(8) =137a(9) =200a(10) =299a(11) =418a(12) =571a(13) =748a(14) =997a(15) =1282a(16) =1639a(17) =2040a(18) =2545a(19) =3106a(20) =3767a(21) =4492a(22) =5401a(23) =6394a(24) =7523a(25) =8744a(26) =10225a(27) =11822a(28) =13625a(29) =15556