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Ingy döt Net 2013-04-10 23:57:08 -07:00
parent 47bf37c096
commit b83f433714
12433 changed files with 156208 additions and 123 deletions
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34
Task/Catalan-numbers/GAP/catalan-numbers.gap Normal file
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Catalan1 := function(n)
return Binomial(2*n, n) - Binomial(2*n, n - 1);
end;
Catalan2 := function(n)
return Binomial(2*n, n)/(n + 1);
end;
Catalan3 := function(n)
local k, c;
c := 1;
k := 0;
while k < n do
k := k + 1;
c := 2*(2*k - 1)*c/(k + 1);
od;
return c;
end;
Catalan4_memo := [1];
Catalan4 := function(n)
if not IsBound(Catalan4_memo[n + 1]) then
Catalan4_memo[n + 1] := Sum([0 .. n - 1], i -> Catalan4(i)*Catalan4(n - 1 - i));
fi;
return Catalan4_memo[n + 1];
end;
# The first fifteen: 0 to 14 !
List([0 .. 14], n -> Catalan1(n));
List([0 .. 14], n -> Catalan2(n));
List([0 .. 14], n -> Catalan3(n));
List([0 .. 14], n -> Catalan4(n));
# Same output for all four:
# [ 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440 ]