|
Search: id:A000564
|
|
|
| A000564 |
|
Number of discordant permutations.
(Formerly M5099 N2208)
|
|
+0
2
|
|
| 20, 371, 2588, 11097, 35645, 94457, 218124, 454220, 872648, 1571715, 2684936, 4388567, 6909867, 10536089, 15624200, 22611330, 32025950, 44499779, 60780420, 81744725, 108412889, 141963273, 183747956, 235309016, 298395540
(list; graph; listen)
|
|
|
OFFSET
|
3,1
|
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
|
|
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^6(2x^7-4x^6+36x^5-29x^4-72x^3-411x^2-231x-20)/((1-x)^7).
a(n)=81/80n^6-405/16n^5+4113/16n^4-21267/16n^3+140357/40n^2-7587/2n, n>6.
|
|
MAPLE
|
rr := n - >81/80*n^6 - 405/16*n^5 + 4113/16*n^4 - 21267/16*n^3 + 140357/40*n^2 - 7587/2*n; seq(rr(n), n=7..40);
A000564:=(-20-231*z-411*z**2-72*z**3-29*z**4+36*z**5-4*z**6+2*z**7)/(z-1)**7; [Conjectured by S. Plouffe in his 1992 dissertation.]
|
|
CROSSREFS
|
Sequence in context: A115100 A049683 A014901 this_sequence A019580 A084329 A097832
Adjacent sequences: A000561 A000562 A000563 this_sequence A000565 A000566 A000567
|
|
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
|
|
|
Search completed in 0.002 seconds
|
