Number of 0..7 arrays x(0..n) of n+1 elements with zero n-1st differences.

Terms

a(0) =1a(1) =8a(2) =22a(3) =64a(4) =182a(5) =454a(6) =1046a(7) =2546a(8) =5056a(9) =11638a(10) =33262a(11) =101112a(12) =191802a(13) =688304a(14) =769106a(15) =1102184a(16) =5220960a(17) =23546744a(18) =49886556a(19) =135889790a(20) =142614238a(21) =121124812a(22) =570957758