449004

Appears in sequences

• Number of Schroeder paths of semilength n (i.e., lattice paths from (0,0) to (2n,0), with steps H=(2,0), U=(1,1) and D(1,-1) and not going below the x-axis) with no UD, UHD, UHHD, UHHHD, ... starting at level zero.at n=10A089387
• Triangle read by rows: T(n,k) is the number of Schroeder paths of length 2n and having k low humps.at n=55A101281
• The number of plane rooted complete ternary trees with 2n+1 unlabeled leaves (hence n internal nodes including the root where n starts at 0) satisfying these two conditions: (1) if one of the three children of any internal node is the greatest in deglex order then that child is not the leftmost child; (2) if one of the three children of any internal node is the smallest in deglex order then that child is not the rightmost child. Deglex order refers to degree-lexicographical order defined inductively on the number of leaves (see details under Comments).at n=11A287211
• Total area under all nonnegative lattice paths from (0,0) to (n,0) such that slopes of adjacent steps differ by at most one, assuming zero slope before and after the paths.at n=14A333678
• a(n) = coefficient of x^n in A(x) such that A(x) = 1 + x*(2*A(x)^3 + A(x^3))/3.at n=11A357538