83315

Appears in sequences

• Triangle read by rows: T(n,k) is number of Dyck paths of semilength n having k ascents of length 3 (0<=k<=floor(n/3)). Also number of ordered trees with n edges that have k vertices of outdegree 3.at n=30A114506
• Number of Dyck paths of semilength n having no ascents of length 3.at n=12A114507
• Number of nX7 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.at n=1A233097
• T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.at n=29A233098
• Number of 2 X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.at n=6A233099
• Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 595", based on the 5-celled von Neumann neighborhood.at n=17A283212
• a(n) = coefficient of x^n in A(x) = Sum_{n>=0} C(x)^n * (1 - C(x)^n)^n, where C(x) = x + C(x)^2 is a g.f. of the Catalan numbers (A000108).at n=12A357792