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A263162
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Number of lattice paths starting at {n}^4 and ending when any component equals 0, using steps that decrement one or more components by one.
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2
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1, 15, 2101, 717795, 328504401, 172924236255, 98788351385893, 59547100211425779, 37279994808479614465, 24006888102075722880975, 15800133137207909144690421, 10580854797781352259168325347, 7186571606168294602440625922385, 4938826696886704892539811529645855
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ c * d^n / (Pi^(3/2) * n^(3/2)), where d = 195 + 138*sqrt(2) + 4*sqrt(4756 + 3363*sqrt(2)) = 780.279406806795145659... and c = sqrt(112232 - 176706*sqrt(2) + sqrt(-24823369828 + 32297875299*sqrt(2)))/2744 = 0.02991158822483794318293134... . - Vaclav Kotesovec, Nov 28 2016
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MAPLE
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g():= seq(convert(n, base, 2)[1..4], n=17..31):
b:= proc(l) option remember;
`if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))
end:
a:= n-> b([n$4]):
seq(a(n), n=0..16);
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MATHEMATICA
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g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 4]], {n, 2^4 + 1, 2^5 - 1}];
b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]];
a[n_] := b[Table[n, {4}]];
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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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