Triangle read by rows: T(n,k) is the number of Motzkin paths of length n having trapezoid weight k.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =3a(6) =1a(7) =6a(8) =2a(9) =1a(10) =12a(11) =8a(12) =1a(13) =24a(14) =22a(15) =4a(16) =1a(17) =48a(18) =58a(19) =20a(20) =1a(21) =96a(22) =149a(23) =69a(24) =8a(25) =1a(26) =192a(27) =373a(28) =221a(29) =48