login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=3..44.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]

FORMULA

G.f.: -x^3*(4*x^3 - 5*x^2 - 20*x - 6) / (x - 1)^4. - Jeffrey Shallit

a(n) = (9/2)*n^3 - (45/2)*n^2 + 29*n. - Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001

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 *)

PROG

(MAGMA) [(9/2)*n^3-(45/2)*n^2+29*n: n in [3..45]]; // Vincenzo Librandi, Feb 10 2016

CROSSREFS

Sequence in context: A078810 A114074 A075337 * A292057 A258156 A182540

Adjacent sequences:  A000558 A000559 A000560 * A000562 A000563 A000564

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

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

Adapted Gf from Vincenzo Librandi, Feb 10 2016

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified February 20 07:15 EST 2018. Contains 299359 sequences. (Running on oeis4.)