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%I M2154 #43 Oct 25 2023 16:16:31
%S 0,1,2,31,264,2783,30818,369321,4745952,65275999,957874226,
%T 14951584189,247524019720,4334022049377,80052395326514,
%U 1555999253409203,31755107852542144,679008663143893773,15182701602959054546,354364531995856105099,8618865446674052425224
%N Number of permutations p of [n] such that (n-p(i)+i) mod n >= 4 for all i.
%C Old name was: Hit polynomials.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Alois P. Heinz, <a href="/A004307/b004307.txt">Table of n, a(n) for n = 4..400</a>
%H Earl Glen Whitehead, Jr., <a href="https://doi.org/10.1017/S1446788700012337">Four-discordant permutations</a>, J. Austral. Math. Soc. Ser. A 28 (1979), no. 3, 369-377.
%H D. Zeilberger, <a href="http://arxiv.org/abs/1401.1089">Automatic Enumeration of Generalized Menage Numbers</a>, 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]
%H D. Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/menages.html">Automatic Enumeration of Generalized Ménage Numbers</a>
%H D. Zeilberger, <a href="/A004307/a004307_1.pdf">Automatic Enumeration of Generalized Ménage Numbers</a> [Local copy, pdf file only, no active links]
%F a(n) ~ exp(-4) * n!. - _Vaclav Kotesovec_, Sep 13 2014
%t (* 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}]];
%t a[n_] := b[n, 4];
%t Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 4, 24}] (* _Jean-François Alcover_, Oct 08 2017 *)
%Y A diagonal of A008305.
%K nonn
%O 4,3
%A _N. J. A. Sloane_
%E More terms from _Vladeta Jovovic_, Oct 02 2003
%E Name changed by _Andrew Howroyd_, Sep 19 2017
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