The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A000500 Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-7 places.
(Formerly M5223 N2273)
6
31, 304, 4230, 43880, 547338, 6924960, 94714620, 1375878816, 21273204330, 348919244768, 6056244249682, 110955673493568, 2140465858763844, 43379533256972640, 921616584567907176, 20485188316420940640, 475499882089797554181, 11506280235885243825696 (list; graph; refs; listen; history; text; internal format)
OFFSET
7,1
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
J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]
FORMULA
a(n) = coefficient of y^7 in sum_0^n sigma_{n, k}(n - k)!(y - 1)^k on y where the sigma_{n, k} have generating function sigma(t, u) = (1 - 2t^2(u^2) - 2t^2(1 + t)u^3 + 3t^4(u^4))(1 - tu)^(-1)(1 - (1 + 2t)u - tu^2 + t^3(u^3))^(-1). - Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
MAPLE
seq(f(n, 7), n=7..30); # code for f(n, k) is given in A000440 - Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001
MATHEMATICA
sigma[t_, u_] := (1-2*t^2*u^2 - 2*t^2*(1+t)*u^3 + 3*t^4*u^4)/((1-t*u)*(1-(1 + 2*t)*u - t*u^2 + t^3*u^3)); ds[t_, n_] := D[sigma[t, u], {u, n}] /. u -> 0; f[n_, k_] := Coefficient[ Sum[ Coefficient[ds[t, n]/n!, t, j]*(n-j)!*(y-1)^j, {j, 0, n}], y, k]; a[n_] := f[n, 7]; Table[Print[an = a[n]]; an, {n, 7, 24}] (* Jean-François Alcover, Jan 25 2013, after Maple code *)
CROSSREFS
Sequence in context: A001298 A027841 A221853 * A141912 A147297 A295975
KEYWORD
nonn
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 June 17 11:50 EDT 2024. Contains 373445 sequences. (Running on oeis4.)