%I M4245 N1773 #47 Sep 08 2022 08:44:28

%S 6,44,145,336,644,1096,1719,2540,3586,4884,6461,8344,10560,13136,

%T 16099,19476,23294,27580,32361,37664,43516,49944,56975,64636,72954,

%U 81956,91669,102120,113336,125344,138171,151844,166390,181836,198209,215536,233844,253160,273511,294924,317426,341044

%N Number of discordant permutations.

%D J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H G. C. Greubel, <a href="/A000561/b000561.txt">Table of n, a(n) for n = 3..1000</a>

%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992

%H J. Riordan, <a href="/A000211/a000211.pdf">Discordant permutations</a>, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F 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]

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

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

%p 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

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

%t LinearRecurrence[{4, -6, 4, -1}, {6, 44, 145, 336}, 50] (* _Jean-François Alcover_, Feb 10 2016 *)

%t 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 *)

%o (Magma) [(9/2)*n^3-(45/2)*n^2+29*n: n in [3..45]]; // _Vincenzo Librandi_, Feb 10 2016

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

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

%K nonn,easy

%O 3,1

%A _N. J. A. Sloane_

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