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A048113
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Triangular array T read by rows: T(h,k) = number of paths consisting of steps from (1,1) to (h,k) such that each step has length 1 directed up or right and each vertex (i,j) satisfies i/2<=j<=2i, for h=0,1,2,... and k=0,1,2,...
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9
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0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 6, 12, 6, 0, 0, 0, 0, 0, 0, 6, 18, 18, 6, 0, 0, 0, 0, 0, 0, 0, 24, 36, 24, 0, 0, 0, 0, 0, 0, 0, 0, 24, 60, 60, 24, 0, 0, 0, 0, 0, 0, 0, 0, 24, 84, 120, 84, 24, 0, 0, 0, 0
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OFFSET
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0,13
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LINKS
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EXAMPLE
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Rows: {0}; {0,0}; {0,1,0}; {0,1,1,0}; ...
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MATHEMATICA
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T[0, 0] = T[0, 1] = T[1, 0] = 0; T[1, 1] = T[2, 1] = T[1, 2] = 1; T[h_, k_] /; Not[h/2 <= k <= 2h] = 0; T[h_, k_] := T[h, k] = If[h-1 >= k/2, T[h-1, k], 0] + If[k-1 >= h/2, T[h, k-1], 0]; row[s_] := Table[T[h, s-h], {h, 0, s}]; Table[row[s], {s, 0, 12}] // Flatten (* Jean-François Alcover, Dec 02 2016 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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