Number of zero-sum -1..1 arrays of n elements with first through third differences also in -1..1.

Terms

a(0) =1a(1) =1a(2) =3a(3) =1a(4) =5a(5) =9a(6) =7a(7) =11a(8) =13a(9) =13a(10) =23a(11) =27a(12) =39a(13) =57a(14) =73a(15) =109a(16) =149a(17) =209a(18) =305a(19) =423a(20) =615a(21) =877a(22) =1249a(23) =1807a(24) =2575a(25) =3709a(26) =5339a(27) =7659a(28) =11065a(29) =15915