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A004307 Number of permutations p of [n] such that n-p(i)+i >= 4 (mod n) for all i.
(Formerly M2154)
7
0, 1, 2, 31, 264, 2783, 30818, 369321, 4745952, 65275999, 957874226, 14951584189, 247524019720, 4334022049377, 80052395326514, 1555999253409203, 31755107852542144, 679008663143893773, 15182701602959054546, 354364531995856105099, 8618865446674052425224 (list; graph; refs; listen; history; text; internal format)
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 Ménage Numbers

D. Zeilberger, Automatic Enumeration of Generalized Menage Numbers, arXiv preprint arXiv:1401.1089 [math.CO], 2014.

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 A152278

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

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Last modified March 30 11:52 EDT 2020. Contains 333125 sequences. (Running on oeis4.)