A000565 Number of discordant permutations. (Formerly M5227 N2275)

31, 696, 5823, 29380, 108933, 327840, 848380, 1958004, 4130895, 8107024, 14990889, 26372124, 44470165, 72305160, 113897310, 174496828, 260846703, 381480456, 547057075, 770735316, 1068589557, 1460069392, 1968505152, 2621661540

Offset

7,1

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=7..30.

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]

Index entries for linear recurrences with constant coefficients, signature (8,-28, 56,-70,56,-28,8,-1).

Formula

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

G.f.: -x^7(12x^7 - 6x^6 + 88x^5 - 131x^4 - 548x^3 - 1123x^2 - 448x - 31) / ((1 - x)^8).

a(n) = 243/560n^7 - 243/16n^6 + 3591/16n^5 - 28737/16n^4 + 82257/10n^3 - 81931/4n^2 + 151931/7n, for n>6. (End)

Maple

pp := n - >243/560*n^7 - 243/16*n^6 + 3591/16*n^5 - 28737/16*n^4 + 82257/10*n^3 - 81931/4*n^2 + 151931/7*n; seq(pp(n), n=0..30); # Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
A000565:=-(12*z**7-6*z**6-131*z**4+88*z**5-1123*z**2-548*z**3-31-448*z)/(z-1)**8; # conjectured by Simon Plouffe in his 1992 dissertation

Mathematica

LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {31, 696, 5823, 29380, 108933, 327840, 848380, 1958004}, 30] (* Jean-François Alcover, Feb 10 2016 *)

Prog

(Magma) [243/560*n^7-243/16*n^6+3591/16*n^5-28737/16*n^4+ 82257/10*n^3 - 81931/4*n^2+151931/7*n: n in [7..45]]; // Vincenzo Librandi, Feb 10 2016

Crossrefs

Sequence in context: A020981 A362512 A006097 * A014930 A196988 A358179

Adjacent sequences: A000562 A000563 A000564 * A000566 A000567 A000568

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