Number of 3Xn 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

Terms

a(0) =27a(1) =324a(2) =1838a(3) =7608a(4) =26314a(5) =80819a(6) =227112a(7) =593400a(8) =1455898a(9) =3378085a(10) =7455007a(11) =15725041a(12) =31840088a(13) =62123439a(14) =117194882a(15) =214407666a(16) =381424761a(17) =661365902a(18) =1120086056a(19) =1856304530a(20) =3015496746a(21) =4808693047a(22) =7537606592a(23) =11627841824