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 A000496 Restricted permutations. (Formerly M5143 N2231) 2
 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 (list; graph; refs; listen; history; text; internal format)
 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 STATUS approved

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Last modified March 31 15:37 EDT 2023. Contains 361668 sequences. (Running on oeis4.)