Number of distinct lines passing through at least two points in a triangular grid of side n.

Terms

a(0) =3a(1) =9a(2) =24a(3) =51a(4) =102a(5) =177a(6) =294a(7) =459a(8) =690a(9) =987a(10) =1380a(11) =1875a(12) =2508a(13) =3279a(14) =4212a(15) =5319a(16) =6648a(17) =8199a(18) =10026a(19) =12141a(20) =14580a(21) =17343a(22) =20496a(23) =24051a(24) =28068a(25) =32547a(26) =37542a(27) =43071a(28) =49218a(29) =55983