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A276902
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Number of positive walks with n steps {-3,-2,-1,0,1,2,3} starting at the origin, ending at altitude 1, and staying strictly above the x-axis.
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10
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0, 1, 3, 12, 56, 284, 1526, 8530, 49106, 289149, 1733347, 10542987, 64904203, 403632551, 2531971729, 16002136283, 101795589297, 651286316903, 4188174878517, 27055199929042, 175488689467350, 1142479579205721, 7462785088260791, 48896570201100002
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OFFSET
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0,3
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LINKS
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MATHEMATICA
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walks[n_, k_, h_] = 0;
walks[1, k_, h_] := Boole[0 < k <= h];
walks[n_, k_, h_] /; n >= 2 && k > 0 := walks[n, k, h] = Sum[walks[n - 1, k + x, h], {x, -h, h}];
(* walks represents the number of positive walks with n steps {-h, -h+1, ... , h} that end at altitude k *)
A276902[n_] := (Do[walks[m, k, 3], {m, n}, {k, 3 m}]; walks[n, 1, 3]) (* Davin Park, Oct 10 2016 *)
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CROSSREFS
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KEYWORD
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nonn,walk
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AUTHOR
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STATUS
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approved
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