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A004307 Number of permutations p of [n] such that (n-p(i)+i) mod n >= 4 for all i.
(Formerly M2154)
8
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
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 [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
KEYWORD
nonn
AUTHOR
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 April 25 09:35 EDT 2024. Contains 371967 sequences. (Running on oeis4.)