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Some folks might think: “you still use RCS”?!? And we will say, hey, at least we switched from SCCS to RCS back in … I think it was around 1994 ... at least we are keeping up! :-) :-) :-) Logs say that SCCS version 18 became RCS version 19 on 1994 March 18. RCS served us well. But now it is time to move on. And so we are switching to git. Calc releases produce a lot of file changes. In the 125 releases of calc since 1996, when I started managing calc releases, there have been 15473 file mods!
60 lines
1.8 KiB
Plaintext
60 lines
1.8 KiB
Plaintext
NAME
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catalan - Catalan number
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SYNOPSIS
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catalan(n)
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TYPES
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n integer
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return integer
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DESCRIPTION
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If n >= 0, this returns the Catalan number for index n:
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catalan(n) = comb(2*n,n)/(n + 1)
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Zero is returned for negative n.
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The Catalan numbers occur in solutions of several elementary
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combinatorial problems, e.g. for n >= 1, catalan(n) is the number of
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ways of using parentheses to express a product of n + 1 letters in
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terms of binary products; it is the number of ways of dissecting a
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convex polygon with n + 2 sides into triangles by nonintersecting
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diagonals; it is the number of integer-component-incrementing paths
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from (x,y) = (0,0) to (x,y) = (n,n) for which always y <= x.
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EXAMPLE
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; print catalan(2), catalan(3), catalan(4), catalan(20)
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2 5 14 6564120420
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LIMITS
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none
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LINK LIBRARY
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NUMBER *qcatalan(NUMBER *n)
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SEE ALSO
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comb, fact, perm
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## Copyright (C) 2000 Ernest Bowen
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##
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## Calc is open software; you can redistribute it and/or modify it under
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## the terms of the version 2.1 of the GNU Lesser General Public License
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## as published by the Free Software Foundation.
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##
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## Calc is distributed in the hope that it will be useful, but WITHOUT
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## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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## Public License for more details.
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##
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## A copy of version 2.1 of the GNU Lesser General Public License is
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## distributed with calc under the filename COPYING-LGPL. You should have
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## received a copy with calc; if not, write to Free Software Foundation, Inc.
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## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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##
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## Under source code control: 2000/12/14 01:33:00
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## File existed as early as: 2000
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##
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## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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