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

Terms

a(0) =5a(1) =21a(2) =55a(3) =111a(4) =479a(5) =837a(6) =1333a(7) =1989a(8) =2827a(9) =5737a(10) =7743a(11) =10165a(12) =13031a(13) =16369a(14) =26119a(15) =32081a(16) =38875a(17) =46541a(18) =55115a(19) =78221a(20) =91467a(21) =106087a(22) =122147a(23) =139713a(24) =184765a(25) =209597a(26) =236519a(27) =265591a(28) =296875a(29) =374751