The number of distinct lines defined by an n X n X n grid of points.

Terms

a(0) =28a(1) =253a(2) =1492a(3) =5485a(4) =17092a(5) =41905a(6) =95140a(7) =191773a(8) =364420a(9) =638785a(10) =1085500a(11) =1745389a(12) =2743084a(13) =4136257a(14) =6101740a(15) =8747821a(16) =12377764a(17) =17066737a(18) =23287564a(19) =31174813a(20) =41276548a(21) =53767873a(22) =69544324a(23) =88722973a(24) =112450132a(25) =140859361a(26) =175324636