|
| |
|
|
A000563
|
|
Number of discordant permutations.
(Formerly M4916 N2109)
|
|
2
| |
|
|
13, 192, 1085, 3880, 10656, 24626, 50380, 94128, 163943, 270004, 424839, 643568, 944146, 1347606, 1878302, 2564152, 3436881, 4532264, 5890369, 7555800, 9577940, 12011194, 14915232, 18355232, 22402123, 27132828, 32630507, 38984800, 46292070
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 5,1
|
|
|
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
| S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
|
|
|
FORMULA
| G.f.:-x^5(8x^5-6x^4+10x^3-128x^2-114x-13)/((1-x)^6).
a(n)=81/40n^5-135/4n^4+1719/8n^3-2487/4n^2+3463/5n, n>4.
|
|
|
MAPLE
| r := n->81/40*n^5-135/4*n^4+1719/8*n^3-2487/4*n^2+3463/5*n; seq(r(n), n=5..40);
A000563:=-(-13-114*z-128*z**2+10*z**3-6*z**4+8*z**5)/(z-1)**6; [Conjectured by S. Plouffe in his 1992 dissertation.]
|
|
|
CROSSREFS
| Sequence in context: A055613 A123808 A103731 * A159196 A177508 A015690
Adjacent sequences: A000560 A000561 A000562 * A000564 A000565 A000566
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms, formulae and Maple code from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 2/17/01
|
| |
|
|
