A000496 Restricted permutations. (Formerly M5143 N2231)

1, 1, 2, 6, 24, 44, 80, 144, 260, 476, 872, 1600, 2940, 5404, 9936, 18272, 33604, 61804, 113672, 209072, 384540, 707276, 1300880, 2392688, 4400836, 8094396, 14887912, 27383136, 50365436, 92636476, 170385040, 313386944, 576408452, 1060180428, 1949975816, 3586564688

Offset

0,3

References

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

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

N. S. Mendelsohn, Permutations with confined displacement, Canad. Math. Bull., 4 (1961), 29-38.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Maple

A000496:=-4*(-6+z+2*z**2+4*z**3+z**4)/(z-1)/(z**3+z**2+z-1); # conjectured by Simon Plouffe in his 1992 dissertation
a:= n-> if n<4 then 0 elif n=4 then 24 else (Matrix([[8, 12, 4, 0]]). Matrix(4, (i, j)-> if (i=j-1) then 1 elif j=1 then [2, 0, 0, -1][i] else 0 fi)^n)[1, 3] fi: seq (a(n), n=4..40); # Alois P. Heinz, Aug 26 2008

Mathematica

a[n_] := Switch[n, 0, 1, 1, 1, 2, 2, 3, 6, 4, 24, _, ({8, 12, 4, 0} . MatrixPower[Table[Which[i == j-1, 1, j == 1, {2, 0, 0, -1}[[i]], True, 0], {i, 1, 4}, {j, 1, 4}], n])[[3]]]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Mar 12 2014, after Alois P. Heinz *)

Crossrefs

Sequence in context: A067653 A090755 A192196 * A004306 A092485 A113904

Adjacent sequences: A000493 A000494 A000495 * A000497 A000498 A000499

Keyword

nonn

Author

N. J. A. Sloane

Status

approved