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A000564 Number of discordant permutations.
(Formerly M5099 N2208)
2
20, 371, 2588, 11097, 35645, 94457, 218124, 454220, 872648, 1571715, 2684936, 4388567, 6909867, 10536089, 15624200, 22611330, 32025950, 44499779, 60780420, 81744725, 108412889, 141963273, 183747956, 235309016, 298395540 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,1

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=6..30.

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 (7,-21, 35,-35,21,-7,1).

FORMULA

From Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001: (Start)

G.f.: -x^6(2x^7 - 4x^6 + 36x^5 - 29x^4 - 72x^3 - 411x^2 - 231x - 20) / ((1 - x)^7).

a(n) = 81/80n^6 - 405/16n^5 + 4113/16n^4 - 21267/16n^3 + 140357/40n^2 - 7587/2n, n>6. (End)

MAPLE

rr := n - >81/80*n^6 - 405/16*n^5 + 4113/16*n^4 - 21267/16*n^3 + 140357/40*n^2 - 7587/2*n; seq(rr(n), n=7..40); # Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001

A000564:=(-20-231*z-411*z**2-72*z**3-29*z**4+36*z**5-4*z**6+2*z**7)/(z-1)**7; # conjectured by Simon Plouffe in his 1992 dissertation

MATHEMATICA

Join[{20}, LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {371, 2588, 11097, 35645, 94457, 218124, 454220}, 30]] (* Jean-François Alcover, Feb 10 2016 *)

PROG

(MAGMA) [20] cat [81/80*n^6-405/16*n^5+4113/16*n^4-21267/16*n^3+140357/40*n^2 - 7587/2*n: n in [7..45]]; // Vincenzo Librandi, Feb 10 2016

CROSSREFS

Sequence in context: A228330 A014901 A290581 * A178352 A266736 A019580

Adjacent sequences:  A000561 A000562 A000563 * A000565 A000566 A000567

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 July 16 23:49 EDT 2019. Contains 325092 sequences. (Running on oeis4.)