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

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000470 Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-5 places.
(Formerly M4901 N2101)
6
13, 72, 595, 4096, 39078, 379760, 4181826, 49916448, 647070333, 9035216428, 135236990388, 2159812592384, 36658601139066, 658942295734944, 12504663617290908, 249823152134646144, 5241223014084306270, 115206851288747267148, 2647678812396326064043 (list; graph; refs; listen; history; text; 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

Table of n, a(n) for n=5..23.

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

FORMULA

a(n) = coefficient of y^5 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, 5), n=5..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 - (1 + 2 t) u - t *u^2 + t^3 (u^3))^(-1); ds[t_, n_] := D[sigma[t, u], {u, n}] /. u -> 0; su[n_] := su[n] = Sum[ Coefficient[ds[t, n]/n!, t, j]*(n - j)!*(y - 1)^j, {j, 0, n}]; f[n_, k_] := Coefficient[su[n], y, k]; Table[f[n, 5], {n, 5, 23}] (* Jean-Fran├žois Alcover, Sep 01 2011, after Maple prog. *)

CROSSREFS

Cf. A000500, A000492, A000440, A000476, A000380, A000388.

Sequence in context: A106173 A094943 A189605 * A297905 A298499 A298318

Adjacent sequences:  A000467 A000468 A000469 * A000471 A000472 A000473

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 19 18:27 EST 2019. Contains 319309 sequences. (Running on oeis4.)