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Search: id:A000563
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| A000563 |
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Number of discordant permutations.
(Formerly M4916 N2109)
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+0
2
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| 13, 192, 1085, 3880, 10656, 24626, 50380, 94128, 163943, 270004, 424839, 643568, 944146, 1347606, 1878302, 2564152, 3436881, 4532264, 5890369, 7555800, 9577940, 12011194, 14915232, 18355232, 22402123, 27132828, 32630507, 38984800, 46292070
(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^5(8x^5-6x^4+10x^3-128x^2-114x-13)/((1-x)^6).
a(n)=81/40n^5-135/4n^4+1719/8n^3-2487/4n^2+3463/5n, n>4.
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MAPLE
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r := n->81/40*n^5-135/4*n^4+1719/8*n^3-2487/4*n^2+3463/5*n; seq(r(n), n=5..40);
A000563:=-(-13-114*z-128*z**2+10*z**3-6*z**4+8*z**5)/(z-1)**6; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Sequence in context: A055613 A123808 A103731 this_sequence A159196 A015690 A027773
Adjacent sequences: A000560 A000561 A000562 this_sequence A000564 A000565 A000566
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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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