login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000562 Number of discordant permutations.
(Formerly M4657 N1994)
2
9, 95, 420, 1225, 2834, 5652, 10165, 16940, 26625, 39949, 57722, 80835, 110260, 147050, 192339, 247342, 313355, 391755, 484000, 591629, 716262, 859600, 1023425, 1209600, 1420069, 1656857, 1922070, 2217895, 2546600, 2910534, 3312127, 3753890, 4238415, 4768375, 5346524, 5975697 (list; graph; refs; listen; history; text; internal format)
OFFSET
4,1
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
From Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001: (Start)
G.f.: -x^4(2x^5 - 4x^4 + 15x^3 - 35x^2 - 50x - 9) / ((1 - x)^5).
a(n) = 27/8n^4 - 135/4n^3 + 921/8n^2 - 539/4n, n>4. (End)
MAPLE
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
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
MATHEMATICA
Join[{9}, LinearRecurrence[{5, -10, 10, -5, 1}, {95, 420, 1225, 2834, 5652}, 40]] (* Jean-François Alcover, Feb 10 2016 *)
PROG
(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
CROSSREFS
Sequence in context: A099297 A057782 A115071 * A193216 A213019 A098450
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 18 22:50 EDT 2024. Contains 370951 sequences. (Running on oeis4.)