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Search: id:A135538
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| A135538 |
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Number of triples in all permutations of order n that are collinear modulo n. |
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+0
2
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| 0, 0, 6, 32, 400, 2304, 35280, 322560, 3888000, 48384000, 731808000, 9858723840, 161902540800, 2628760780800, 43181994240000, 876764528640000, 16124496740352000, 358721232629760000, 6933770723303424000, 168738115888742400000, 3644128675321085952000, 94201965756599500800000
(list; graph; listen)
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OFFSET
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1,3
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LINKS
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L. Li, Collinear triples in permutations, arXiv:0802.0572
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FORMULA
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For n>=3, a(n) = (n-3)! * A146557(n).
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EXAMPLE
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For example, in a permutation p=[5,2,4,3,1], a triple of points { (2,p(2)=2), (4,p(4)=3), (5,p(5)=1) } is collinear, since they are located on the line: x + 3*y == 3 (mod 5).
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PROGRAM
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(PARI) { a(n) = if(n<3, 0, (n-3)! * n * sum(i=1, n, sum(j=1, n-i-1, (n-i-j) * (n*gcd([i, j, n-i-j]) - gcd(i, n) - gcd(j, n) - gcd(i+j, n) + 2) ))) }
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CROSSREFS
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Sequence in context: A146557 A020013 A121120 this_sequence A132548 A140521 A069065
Adjacent sequences: A135535 A135536 A135537 this_sequence A135539 A135540 A135541
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KEYWORD
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nonn
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AUTHOR
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R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 22 2008, corrected Oct 24 2008
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EXTENSIONS
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Edited and extended by Max Alekseyev, Oct 31 2008
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