Number of 3X3X3 triangular 0..n arrays with every horizontal row having the same average value.

Terms

a(0) =2a(1) =23a(2) =62a(3) =157a(4) =312a(5) =601a(6) =986a(7) =1619a(8) =2426a(9) =3589a(10) =5028a(11) =6997a(12) =9314a(13) =12371a(14) =15914a(15) =20377a(16) =25488a(17) =31789a(18) =38846a(19) =47399a(20) =56906a(21) =68161a(22) =80592a(23) =95137a(24) =111002a(25) =129383a(26) =149342a(27) =172141a(28) =196800a(29) =224761