A004307 Number of permutations p of [n] such that (n-p(i)+i) mod n >= 4 for all i. (Formerly M2154)

0, 1, 2, 31, 264, 2783, 30818, 369321, 4745952, 65275999, 957874226, 14951584189, 247524019720, 4334022049377, 80052395326514, 1555999253409203, 31755107852542144, 679008663143893773, 15182701602959054546, 354364531995856105099, 8618865446674052425224

Offset

4,3

Comments

Old name was: Hit polynomials.

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Alois P. Heinz, Table of n, a(n) for n = 4..400

Earl Glen Whitehead, Jr., Four-discordant permutations, J. Austral. Math. Soc. Ser. A 28 (1979), no. 3, 369-377.

D. Zeilberger, Automatic Enumeration of Generalized Menage Numbers, arXiv preprint arXiv:1401.1089 [math.CO], 2014. [This is a different document from the one with the same title on Doron Zeilberger's web site]

D. Zeilberger, Automatic Enumeration of Generalized Ménage Numbers

D. Zeilberger, Automatic Enumeration of Generalized Ménage Numbers [Local copy, pdf file only, no active links]

Formula

a(n) ~ exp(-4) * n!. - Vaclav Kotesovec, Sep 13 2014

Mathematica

(* Very slow *) b[n_, n0_] := Permanent[Table[If[(0 <= j-i && j-i < n-n0) || j-i < -n0, 1, 0], {i, 1, n}, {j, 1, n}]];
a[n_] := b[n, 4];
Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 4, 24}] (* Jean-François Alcover, Oct 08 2017 *)

Crossrefs

A diagonal of A008305.

Sequence in context: A223145 A188225 A164676 * A268879 A120357 A333935

Adjacent sequences: A004304 A004305 A004306 * A004308 A004309 A004310

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, Oct 02 2003

Name changed by Andrew Howroyd, Sep 19 2017

Status

approved