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A000561
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Number of discordant permutations.
(Formerly M4245 N1773)
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3
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6, 44, 145, 336, 644, 1096, 1719, 2540, 3586, 4884, 6461, 8344, 10560, 13136, 16099, 19476, 23294, 27580, 32361, 37664, 43516, 49944, 56975, 64636, 72954, 81956, 91669, 102120, 113336, 125344, 138171, 151844, 166390, 181836, 198209, 215536, 233844, 253160, 273511, 294924, 317426, 341044
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,1
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REFERENCES
| J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| 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
| G.f.: -(4x^3 - 5x^2 -20x -6)/(x-1)^4 (Jeffrey Shallit).
a(n)=(9/2)n^3-(45/2)n^2+29n.
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MAPLE
| f := n->9/2*n^3-45/2*n^2+29*n; seq(f(n), n=0..50);
A000561:=-(-6-20*z-5*z**2+4*z**3)/(z-1)**4; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
| Sequence in context: A078810 A114074 A075337 * A091162 A156002 A091163
Adjacent sequences: A000558 A000559 A000560 * A000562 A000563 A000564
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms, formula and Maple code from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 2/17/01
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