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

Terms

a(0) =9a(1) =37a(2) =167a(3) =527a(4) =1341a(5) =3067a(6) =6019a(7) =11353a(8) =19601a(9) =32099a(10) =50621a(11) =75931a(12) =112125a(13) =159765a(14) =222517a(15) =304463a(16) =406447a(17) =538245a(18) =699187a(19) =897049a(20) =1138935a(21) =1425355a(22) =1774971a(23) =2184135a(24) =2666551a(25) =3233507a(26) =3883865a(27) =4649645a(28) =5521247a(29) =6521027