Number of zero-sum -n..n arrays of 5 elements with first through third differences also in -n..n.

Terms

a(0) =5a(1) =21a(2) =95a(3) =239a(4) =529a(5) =1041a(6) =1785a(7) =3009a(8) =4655a(9) =6937a(10) =10007a(11) =13823a(12) =18963a(13) =25151a(14) =32837a(15) =42225a(16) =53147a(17) =66679a(18) =82163a(19) =100347a(20) =121523a(21) =145299a(22) =173373a(23) =204621a(24) =240115a(25) =280223a(26) =324311a(27) =374807a(28) =429953a(29) =491279