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A276903
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Number of positive walks with n steps {-2,-1,0,1,2} starting at the origin, ending at altitude 2, and staying strictly above the x-axis.
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10
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0, 1, 2, 7, 25, 96, 382, 1567, 6575, 28096, 121847, 534953, 2373032, 10619922, 47890013, 217395690, 992640367, 4555957948, 21007405327, 97266928685, 452046424465, 2108022305795, 9860773604035, 46256877824220, 217555982625385, 1025667805621986, 4846240583558277
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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 *)
A276903[n_] := (Do[walks[m, k, 2], {m, n}, {k, 2 m}]; walks[n, 2, 2]) (* 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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