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A000563 Number of discordant permutations.
(Formerly M4916 N2109)
2
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; refs; listen; history; text; internal format)
OFFSET
5,1
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).
LINKS
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]
FORMULA
From Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001: (Start)
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. (End)
MAPLE
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); # Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
A000563:=-(-13-114*z-128*z**2+10*z**3-6*z**4+8*z**5)/(z-1)**6; # conjectured by Simon Plouffe in his 1992 dissertation
MATHEMATICA
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {13, 192, 1085, 3880, 10656, 24626}, 30] (* Jean-François Alcover, Feb 10 2016 *)
PROG
(Magma) [81/40*n^5-135/4*n^4+1719/8*n^3-2487/4*n^2+3463/5*n: n in [5..45]]; // Vincenzo Librandi, Feb 10 2016
CROSSREFS
Sequence in context: A123808 A103731 A331495 * A213698 A159196 A177508
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
STATUS
approved

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)