Number of zero-sum -3..3 arrays of n elements with first through fourth differences also in -3..3.

Terms

a(0) =1a(1) =3a(2) =15a(3) =29a(4) =55a(5) =167a(6) =295a(7) =647a(8) =1427a(9) =3399a(10) =6987a(11) =15915a(12) =35035a(13) =78815a(14) =175659a(15) =401885a(16) =907063a(17) =2070241a(18) =4703563a(19) =10756853a(20) =24527921a(21) =56167839a(22) =128565473a(23) =295006361a(24) =677007927a(25) =1556684111a(26) =3580113745a(27) =8243974707a(28) =18993055553a(29) =43795271957