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A276901
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Number of positive walks with n steps {-3,-2,-1,1,2,3} 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, 9, 34, 159, 730, 3579, 17762, 90538, 467796, 2452727, 12997554, 69549847, 375159290, 2038068813, 11140256754, 61227097438, 338140106124, 1875581756078, 10444142352812, 58364192607047, 327203347219250, 1839778650617309, 10372512509521074
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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}] + Sum[walks[n - 1, k + x, h], {x, h}];
(* walks represents the number of positive walks with n steps {-h, -h+1, ... -1, 1, ..., h} that end at altitude k *)
A276901[n_] := (Do[walks[m, k, 3], {m, n}, {k, 3 m}]; walks[n, 2, 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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