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A000382
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Restricted permutations.
(Formerly M4087 N1696)
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3
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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
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OFFSET
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4,1
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COMMENTS
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The fourth column of A008305, divided by 4.
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REFERENCES
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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).
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LINKS
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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
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FORMULA
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a(n) = a(n-1)+a(n-2)+a(n-3)-2 (conjectured).
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MAPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A008305, A000496 divided by 4, A020992.
Sequence in context: A007745 A188556 A021011 * A208670 A208726 A192750
Adjacent sequences: A000379 A000380 A000381 * A000383 A000384 A000385
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Vincenzo Librandi, Mar 14 2014
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STATUS
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approved
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