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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

Table of n, a(n) for n=5..33.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]

Index entries for linear recurrences with constant coefficients, signature (6,-15, 20,-15,6,-1).

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

Adjacent sequences:  A000560 A000561 A000562 * A000564 A000565 A000566

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001

STATUS

approved

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Last modified May 26 08:39 EDT 2020. Contains 334620 sequences. (Running on oeis4.)