A000382 Restricted permutations. (Formerly M4087 N1696)

6, 11, 20, 36, 65, 119, 218, 400, 735, 1351, 2484, 4568, 8401, 15451, 28418, 52268, 96135, 176819, 325220, 598172, 1100209, 2023599, 3721978, 6845784, 12591359, 23159119, 42596260, 78346736, 144102113, 265045107, 487493954

Offset

4,1

Comments

The fourth column of A008305, divided by 4.

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 = 4..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

Formula

a(n) = a(n-1)+a(n-2)+a(n-3)-2 (conjectured).

Maple

A000382:=-(-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 6 else (Matrix([[11, 7, 4, 2]]). Matrix(4, (i, j)-> if (i=j-1) then 1 elif j=1 then [2, 0, 0, -1][i] else 0 fi)^(n-2))[1, 4] fi: seq(a(n), n=4..30); # Alois P. Heinz, Aug 26 2008

Mathematica

a[n_] := Which[n<4, 0, n == 4, 6, True, {11, 7, 4, 2}.MatrixPower[Table[Which[i == j-1, 1, j == 1, {2, 0, 0, -1}[[i]], True, 0], {i, 1, 4}, {j, 1, 4}], n-2] // Last]; Table[a[n], {n, 4, 27}] (* Jean-François Alcover, Mar 12 2014, after Alois P. Heinz *)

Crossrefs

Cf. A008305, A000496 divided by 4, A020992.

Sequence in context: A007745 A188556 A021011 * A208670 A208726 A192750

Adjacent sequences: A000379 A000380 A000381 * A000383 A000384 A000385

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Mar 14 2014

Status

approved