Number of zero-sum -n..n arrays of 4 elements with first through third differences also in -n..n.

Terms

a(0) =1a(1) =15a(2) =29a(3) =75a(4) =115a(5) =217a(6) =297a(7) =479a(8) =609a(9) =887a(10) =1091a(11) =1493a(12) =1765a(13) =2315a(14) =2689a(15) =3399a(16) =3875a(17) =4777a(18) =5373a(19) =6491a(20) =7213a(21) =8555a(22) =9439a(23) =11041a(24) =12061a(25) =13947a(26) =15157a(27) =17331a(28) =18719a(29) =21221