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A000496
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Restricted permutations.
(Formerly M5143 N2231)
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2
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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
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OFFSET
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0,3
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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 = 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
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MAPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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Sequence in context: A067653 A090755 A192196 * A004306 A092485 A113904
Adjacent sequences: A000493 A000494 A000495 * A000497 A000498 A000499
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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