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Search: id:A047929
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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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COMMENT
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Comment from Asher Natan Auel (auela(AT)reed.edu) Jan 26 2000: 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.
a(n)=A004320(n)*6. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2007
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LINKS
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Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Index entries for sequences related to parenthesizing
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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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MAPLE
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a:=n->sum(sum((n^2-n), j=0..n), k=0..n): seq(a(n), n=1..33); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2007
a:=n->(sum((numbperm(n, 3)), j=1..n)):seq(a(n), n=2..34); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 12 2008
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CROSSREFS
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Cf. A045991.
Equals 6 * A004320(n-2).
Sequence in context: A117735 A041624 A034725 this_sequence A118864 A118606 A044269
Adjacent sequences: A047926 A047927 A047928 this_sequence A047930 A047931 A047932
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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