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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 non-intersecting
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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) 2000,2021 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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