T(n,k)=Number of side-n hexagonal 0..k arrays with values nondecreasing E, SW and SE.

Terms

a(0) =2a(1) =3a(2) =10a(3) =4a(4) =53a(5) =52a(6) =5a(7) =200a(8) =1211a(9) =260a(10) =6a(11) =606a(12) =17336a(13) =27768a(14) =1256a(15) =7a(16) =1572a(17) =175869a(18) =1664244a(19) =618013a(20) =5908a(21) =8a(22) =3630a(23) =1374208a(24) =64697626a(25) =161114424a(26) =13312100a(27) =27224a(28) =9a(29) =7656