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Search: id:A000561
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| A000561 |
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Number of discordant permutations.
(Formerly M4245 N1773)
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+0
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; listen)
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OFFSET
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3,1
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REFERENCES
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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.
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.: -(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
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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
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Sequence in context: A078810 A114074 A075337 this_sequence A091162 A091163 A102591
Adjacent sequences: A000558 A000559 A000560 this_sequence A000562 A000563 A000564
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KEYWORD
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nonn
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AUTHOR
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njas
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EXTENSIONS
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More terms, formula and Maple code from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 2/17/01
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