41835

Appears in sequences

• Motzkin numbers: number of ways of drawing any number of nonintersecting chords joining n (labeled) points on a circle.at n=13A001006
• Number of unlabeled identity unit interval graphs.at n=15A005219
• Table where the entry (n,k) (n >= 0, k >= 0) gives number of Motzkin paths of the length n with the minimum peak width of k.at n=91A064645
• Expansion of (1 + x - sqrt(1 - 2*x - 3*x^2)) / 2 in powers of x.at n=15A086246
• Triangle read by rows: T(n,k)=number of ordered trees with n edges and k branch nodes at odd height.at n=35A091958
• Number of (s(0), s(1), ..., s(n)) such that 0 < s(i) < 8 and |s(i) - s(i-1)| <= 1 for i = 1,2,...,n, s(0) = 1, s(n) = 1.at n=13A094288
• Triangle read by rows: counts Motzkin paths by length of final descent.at n=56A098979
• Triangle read by rows: counts Motzkin paths by length of final descent.at n=57A098979
• Bisection of Motzkin numbers A001006.at n=6A099250
• Triangle read by rows: T(n,k) is the number of short bushes with n edges and having the leftmost leaf at height k (a short bush is an ordered tree with no nodes of outdegree 1).at n=49A106489
• Triangle read by rows: T(n,k) is number of Grand Motzkin paths of length n having k returns to the x-axis from above (i.e., d steps hitting the x-axis).at n=49A109195
• Triangle read by rows: T(n,k) is the number of paths in the first quadrant from (0,0) to (n,0), consisting of steps U=(1,1), D=(1,-1), h=(1,0) and H=(2,0), having k H steps (0<=k<=floor(n/2)).at n=49A132280
• Odd Motzkin numbers.at n=9A134717
• Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, -1), (-1, 0, 0), (-1, 1, 1), (0, 0, 1), (1, 0, -1)}.at n=11A148294
• Expansion of (3 -x -sqrt(1-2*x-3*x^2))/2.at n=15A168049
• Triangle read by rows: T(n,k) is the number of involutions of {1,2,...,n} having genus k (see first comment for definition of genus).at n=78A178515
• A permutation of Motzkin numbers by reversal of indices in blocks of length 7.at n=8A180352
• Number of strings of numbers x(i=1..n) in 0..8 with sum i^3*x(i) equal to n^3*8.at n=8A184256
• Number of zero-sum -n..n arrays of 4 elements with first and second differences also in -n..n.at n=33A201875
• Number of nonnegative integer arrays of length n+3 with new values 0 upwards introduced in order, and containing the value n-1.at n=9A211563