Number of ways to choose 4 points in an n X n X n triangular grid.

Terms

a(0) =15a(1) =210a(2) =1365a(3) =5985a(4) =20475a(5) =58905a(6) =148995a(7) =341055a(8) =720720a(9) =1426425a(10) =2672670a(11) =4780230a(12) =8214570a(13) =13633830a(14) =21947850a(15) =34389810a(16) =52602165a(17) =78738660a(18) =115584315a(19) =166695375a(20) =236561325a(21) =330791175a(22) =456326325a(23) =621682425a(24) =837222750a(25) =1115465715a(26) =1471429260a(27) =1923014940