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%I M5143 N2231 #45 Apr 13 2022 13:25:15
%S 1,1,2,6,24,44,80,144,260,476,872,1600,2940,5404,9936,18272,33604,
%T 61804,113672,209072,384540,707276,1300880,2392688,4400836,8094396,
%U 14887912,27383136,50365436,92636476,170385040,313386944,576408452,1060180428,1949975816,3586564688
%N Restricted permutations.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A000496/b000496.txt">Table of n, a(n) for n = 0..1000</a>
%H N. S. Mendelsohn, <a href="http://dx.doi.org/10.4153/CMB-1961-005-4">Permutations with confined displacement</a>, Canad. Math. Bull., 4 (1961), 29-38.
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%p 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
%p 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
%t 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_ *)
%K nonn
%O 0,3
%A _N. J. A. Sloane_
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