Number of -n..n arrays x(0..3) of 4 elements with zeroth through 3rd differences all nonzero.

Terms

a(0) =2a(1) =104a(2) =660a(3) =2474a(4) =6604a(5) =14696a(6) =28490a(7) =50448a(8) =83092a(9) =129642a(10) =193292a(11) =278240a(12) =388258a(13) =528328a(14) =703140a(15) =918330a(16) =1179228a(17) =1492584a(18) =1864202a(19) =2301584a(20) =2811588a(21) =3402266a(22) =4081084a(23) =4857344a(24) =5738882a(25) =6735720a(26) =7856884a(27) =9112842a(28) =10513196a(29) =12069800