Number of zero-sum -n..n arrays of 6 elements with first through third differences also in -n..n.

Terms

a(0) =9a(1) =53a(2) =255a(3) =883a(4) =2369a(5) =5429a(6) =11015a(7) =20519a(8) =35743a(9) =58863a(10) =92683a(11) =140431a(12) =206133a(13) =294575a(14) =410949a(15) =561639a(16) =753393a(17) =994367a(18) =1293591a(19) =1660765a(20) =2107089a(21) =2644313a(22) =3285935a(23) =4046931a(24) =4942529a(25) =5990419a(26) =7208417a(27) =8617099a(28) =10238327a(29) =12094665