Triangle read by rows: T(n,k) is number of Grand Motzkin paths of length n having k hills (i.e., ud's starting at level 0). (A Grand Motzkin path is a path in the half-plane x>=0, starting at (0,0), ending at (n,0) and consisting of steps u=(1,1), d=(1,-1) and h=(1,0).).

A109191

Triangle read by rows: T(n,k) is number of Grand Motzkin paths of length n having k hills (i.e., ud's starting at level 0). (A Grand Motzkin path is a path in the half-plane x>=0, starting at (0,0), ending at (n,0) and consisting of steps u=(1,1), d=(1,-1) and h=(1,0).).

Terms

    a(0) =1a(1) =1a(2) =2a(3) =1a(4) =5a(5) =2a(6) =13a(7) =5a(8) =1a(9) =34a(10) =14a(11) =3a(12) =91a(13) =40a(14) =9a(15) =1a(16) =247a(17) =114a(18) =28a(19) =4a(20) =678a(21) =327a(22) =87a(23) =14a(24) =1a(25) =1877a(26) =942a(27) =267a(28) =48a(29) =5

External references