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

Terms

a(0) =3a(1) =6a(2) =12a(3) =21a(4) =36a(5) =57a(6) =90a(7) =129a(8) =186a(9) =261a(10) =354a(11) =465a(12) =612a(13) =783a(14) =990a(15) =1233a(16) =1524a(17) =1863a(18) =2262a(19) =2703a(20) =3216a(21) =3801a(22) =4458a(23) =5187a(24) =6024a(25) =6951a(26) =7986a(27) =9129a(28) =10392a(29) =11775