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A286761
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Total number of nodes summed over all lattice paths from (0,0) to (n,0) that do not go below the x-axis or above the diagonal x=y and consist of steps D=(1,-1), H=(1,0) and S=(0,1).
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2
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1, 2, 7, 25, 106, 470, 2218, 10799, 54158, 277089, 1441956, 7602630, 40524952, 217954222, 1181107568, 6441519814, 35323986620, 194629681327, 1076819450324, 5979314763974, 33308210757892, 186074808452033, 1042146006514656, 5850075202736100, 32907053660222560
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OFFSET
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0,2
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LINKS
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MAPLE
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b:= proc(x, y) option remember; `if`(y<0 or y>x, 0, `if`(x=0, [1$2],
(p-> p+[0, p[1]])(b(x-1, y)+b(x, y-1)+b(x-1, y+1))))
end:
a:= n-> b(n, 0)[2]:
seq(a(n), n=0..30);
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MATHEMATICA
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b[x_, y_] := b[x, y] = If[y < 0 || y > x, 0, If[x == 0, {1, 1}, Function[
p, p + {0, p[[1]]}][b[x - 1, y] + b[x, y - 1] + b[x - 1, y + 1]]]];
a[n_] := b[n, 0][[2]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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