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A047929
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a(n) = n^2*(n-1)*(n-2).
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5
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0, 18, 96, 300, 720, 1470, 2688, 4536, 7200, 10890, 15840, 22308, 30576, 40950, 53760, 69360, 88128, 110466, 136800, 167580, 203280, 244398, 291456, 345000, 405600, 473850, 550368, 635796, 730800, 836070, 952320, 1080288, 1220736
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OFFSET
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2,2
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COMMENTS
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There are 5 ways to put parentheses in the expression a - b - c - d: (a - (b - c)) - d, ((a - b) - c) - d, (a - b) - (c - d), a - (b - (c - d)), a - ((b - c) - d). A047929 describes how many sets of natural numbers [a,b,c,d] can be produced with the numbers {0,1,2,3,...n} such that all the distinct expressions take different values. A045991 describes the similar process for a - b - c. - Asher Natan Auel (auela(AT)reed.edu), Jan 26 2000
For n >= 3, a(n)/6 is the number of permutations of n symbols that 3-commute with an n-cycle (see A233440 for definition). - Luis Manuel Rivera MartÃnez, Feb 24 2014
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 2..1000
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
Index entries for sequences related to parenthesizing
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
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a(n) = A004320(n-2)*6.
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EXAMPLE
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For example, no such sets can be produced with only 0's or only 0's and 1's; with {0,1,2,3}, 18 such sets can be produced.
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PROG
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(MAGMA) [n^2*(n-1)*(n-2): n in [2..40]]; // Vincenzo Librandi, May 02 2011
(PARI) a(n)=n^4 - 3*n^3 + 2*n^2 \\ Charles R Greathouse IV, May 02, 2011
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CROSSREFS
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Cf. A045991.
Sequence in context: A186122 A275253 A034725 * A243995 A264202 A338783
Adjacent sequences: A047926 A047927 A047928 * A047930 A047931 A047932
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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