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A000561 Number of discordant permutations.
(Formerly M4245 N1773)
3
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; text; internal format)
OFFSET

3,1

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

G. C. Greubel, Table of n, a(n) for n = 3..1000

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 (4,-6,4,-1).

FORMULA

G.f.: x^3*(6 + 20*x + 5*x^2 - 4*x^3) / (1 - x)^4. - Jeffrey Shallit [adapted by Vincenzo Librandi, Feb 10 2016]

a(n) = n*(9*n^2 - 45*n + 58)/2. - Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001

E.g.f.: x*(-22 - 4*x + (22 - 18*x + 9*x^2)*exp(x))/2. - G. C. Greubel, Nov 23 2018

MAPLE

f := n->9/2*n^3-45/2*n^2+29*n; seq(f(n), n=0..50); # Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001

A000561:=-(-6-20*z-5*z**2+4*z**3)/(z-1)**4; # conjectured by Simon Plouffe in his 1992 dissertation

MATHEMATICA

LinearRecurrence[{4, -6, 4, -1}, {6, 44, 145, 336}, 50] (* Jean-François Alcover, Feb 10 2016 *)

PROG

(MAGMA) [(9/2)*n^3-(45/2)*n^2+29*n: n in [3..45]]; // Vincenzo Librandi, Feb 10 2016

(PARI) for(n=3, 45, print1(n*(9*n^2 - 45*n + 58)/2, ", ")) \\ G. C. Greubel, Nov 23 2018

(Sage) [n*(9*n^2 - 45*n + 58)/2 for n in (3..45)] # G. C. Greubel, Nov 23 2018

CROSSREFS

Sequence in context: A078810 A114074 A075337 * A292057 A258156 A182540

Adjacent sequences:  A000558 A000559 A000560 * A000562 A000563 A000564

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 January 23 04:40 EST 2019. Contains 319370 sequences. (Running on oeis4.)