A000562 - OEIS

%I M4657 N1994 #38 Sep 08 2022 08:44:28

%S 9,95,420,1225,2834,5652,10165,16940,26625,39949,57722,80835,110260,

%T 147050,192339,247342,313355,391755,484000,591629,716262,859600,

%U 1023425,1209600,1420069,1656857,1922070,2217895,2546600,2910534,3312127,3753890,4238415,4768375,5346524,5975697

%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 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_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10, 10,-5,1).

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

%F G.f.: -x^4(2x^5 - 4x^4 + 15x^3 - 35x^2 - 50x - 9) / ((1 - x)^5).

%F a(n) = 27/8n^4 - 135/4n^3 + 921/8n^2 - 539/4n, n>4. (End)

%p ff := n->27/8*n^4-135/4*n^3+921/8*n^2-539/4*n; seq(ff(n), n=5..40); # Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001

%p A000562:=(-9-50*z-35*z**2+15*z**3-4*z**4+2*z**5)/(z-1)**5; # conjectured by _Simon Plouffe_ in his 1992 dissertation

%t Join[{9}, LinearRecurrence[{5, -10, 10, -5, 1}, {95, 420, 1225, 2834, 5652}, 40]] (* _Jean-François Alcover_, Feb 10 2016 *)

%o (Magma) [9] cat [27/8*n^4-135/4*n^3+921/8*n^2-539/4*n: n in [5..45]]; // _Vincenzo Librandi_, Feb 10 2016

%K nonn,easy

%O 4,1

%A _N. J. A. Sloane_

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