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A357654
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Number of lattice paths from (0,0) to (i,n-2*i) that do not go above the diagonal x=y using steps in {(1,0), (0,1)}.
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3
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1, 0, 1, 1, 1, 2, 3, 3, 6, 9, 10, 19, 29, 34, 63, 97, 118, 215, 333, 416, 749, 1165, 1485, 2650, 4135, 5355, 9490, 14845, 19473, 34318, 53791, 71313, 125104, 196417, 262735, 459152, 721887, 973027, 1694914, 2667941, 3619955, 6287896, 9907851, 13521307, 23429158
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OFFSET
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0,6
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LINKS
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FORMULA
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MAPLE
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b:= proc(x, y) option remember; `if`(min(x, y)<0 or y>x, 0,
`if`(max(x, y)=0, 1, b(x-1, y)+b(x, y-1)))
end:
a:= n-> add(b(i, n-2*i), i=ceil(n/3)..floor(n/2)):
seq(a(n), n=0..44);
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MATHEMATICA
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A120730[n_, k_]:= If[n>2*k, 0, Binomial[n, k]*(2*k-n+1)/(k+1)];
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PROG
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(Magma)
A120730:= func< n, k | n gt 2*k select 0 else Binomial(n, k)*(2*k-n+1)/(k+1) >;
(SageMath)
def A120730(n, k): return 0 if (n>2*k) else binomial(n, k)*(2*k-n+1)/(k+1)
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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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