|
|
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
|
|
|
FORMULA
|
a(n) = n*(9*n^2 - 45*n + 58)/2. - Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
E.g.f.: x*(-22 - 4*x + (22 - 18*x + 9*x^2)*exp(x))/2. - G. C. Greubel, Nov 23 2018
|
|
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
|
|
MATHEMATICA
|
Drop[CoefficientList[Series[x^3(6+20x+5x^2-4x^3)/(1-x)^4, {x, 0, 50}], x], 3] (* Harvey P. Dale, Jul 20 2021 *)
|
|
PROG
|
(PARI) for(n=3, 45, print1(n*(9*n^2 - 45*n + 58)/2, ", ")) \\ G. C. Greubel, Nov 23 2018
(Sage) [n*(9*n^2 - 45*n + 58)/2 for n in (3..45)] # G. C. Greubel, Nov 23 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
|
|
STATUS
|
approved
|
|
|
|