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Search: id:A000562
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| A000562 |
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Number of discordant permutations.
(Formerly M4657 N1994)
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+0
2
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| 9, 95, 420, 1225, 2834, 5652, 10165, 16940, 26625, 39949, 57722, 80835, 110260, 147050, 192339, 247342, 313355, 391755, 484000, 591629, 716262, 859600, 1023425, 1209600, 1420069, 1656857, 1922070, 2217895, 2546600, 2910534, 3312127, 3753890, 4238415, 4768375, 5346524, 5975697
(list; graph; listen)
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OFFSET
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3,1
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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G.f.:-x^4(2x^5-4x^4+15x^3-35x^2-50x-9)/((1-x)^5).
a(n)=27/8n^4-135/4n^3+921/8n^2-539/4n, n>4.
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MAPLE
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ff := n->27/8*n^4-135/4*n^3+921/8*n^2-539/4*n; seq(ff(n), n=5..40);
A000562:=(-9-50*z-35*z**2+15*z**3-4*z**4+2*z**5)/(z-1)**5; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Sequence in context: A099297 A057782 A115071 this_sequence A098450 A065456 A052389
Adjacent sequences: A000559 A000560 A000561 this_sequence A000563 A000564 A000565
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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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EXTENSIONS
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More terms, formulae and Maple code from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 2/17/01
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