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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
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
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 *)
Drop[CoefficientList[Series[x^3(6+20x+5x^2-4x^3)/(1-x)^4, {x, 0, 50}], x], 3] (* Harvey P. Dale, Jul 20 2021 *)
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
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 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)