22767

Appears in sequences

• Expansion of Product_{m>=1} (1 + q^m)^(3*m).at n=11A027346
• a(n) = 3*a(n-1) + 5*a(n-2), with a(0)=2, a(1)=3.at n=7A072263
• 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, -1, 1), (-1, 0, 1), (1, 0, 0), (1, 1, 0)}.at n=8A150313
• Triangle read by rows: T(n,k) is the number of weighted lattice paths in B(n) having k valleys. The members of B(n) are paths of weight n that start at (0,0), end on but never go below the horizontal axis, and whose steps are of the following four kinds: an (1,0)-step with weight 1, an (1,0)-step with weight 2, a (1,1)-step with weight 2, and a (1,-1)-step with weight 1. The weight of a path is the sum of the weights of its steps. A valley is a (1,-1)-step followed by a (1,1)-step.at n=29A182900
• Number of weighted lattice paths in B(n) having no valleys. The members of B(n) are paths of weight n that start at (0,0), end on but never go below the horizontal axis, and whose steps are of the following four kinds: an (1,0)-step with weight 1, an (1,0)-step with weight 2, a (1,1)-step with weight 2, and a (1,-1)-step with weight 1. The weight of a path is the sum of the weights of its steps. A valley is a (1,-1)-step followed by a (1,1)-step.at n=14A182901
• Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock summing to 4.at n=7A183625
• Number of (n+1) X 9 0..2 arrays with every 2 X 2 subblock summing to 4.at n=1A183631
• T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock summing to 4.at n=37A183632
• T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock summing to 4.at n=43A183632
• G.f. satisfies: A(x) = exp( Sum_{n>=1} A(x^n)/(1+x^n) * x^n/n ).at n=18A198518
• G.f.: x^(k^2)/(mul(1-x^(2*i),i=1..k)*mul(1+x^(2*r-1),r=1..oo)) with k=4.at n=56A246580
• Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 617", based on the 5-celled von Neumann neighborhood.at n=26A273248