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%I #28 Mar 05 2017 05:37:02
%S 1,0,1,1,1,3,2,5,6,8,14,16,27,36,51,77,103,155,216,309,448,628,912,
%T 1292,1849,2652,3769,5413,7713,11031,15778,22513,32222,46004,65766,
%U 94004,134283,191992,274291,392041,560287,800615,1144320,1635193,2336976
%N Number of permutations satisfying -k <= p(i) - i <= r and p(i) - i not in I, i=1..n, with k=1, r=4, I={0,3}.
%C Number of compositions (ordered partitions) of n into elements of the set {2,3,5}.
%C For n>=2, a(n) is number of compositions of n-2 with elements from the set {1,2,3} such that no two odd numbers appear consecutively. - _Armend Shabani_, Mar 01 2017
%D D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.
%H Vladimir Baltic, <a href="http://pefmath.etf.rs/vol4num1/AADM-Vol4-No1-119-135.pdf">On the number of certain types of strongly restricted permutations</a>, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (2010), 119-135
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,0,1).
%F a(n) = a(n-2) + a(n-3) + a(n-5).
%F G.f.: -1/(x^5 + x^3 + x^2 - 1).
%t CoefficientList[Series[-1/(x^5 + x^3 + x^2 - 1), {x, 0, 44}], x] (* _Michael De Vlieger_, Mar 02 2017 *)
%Y Row sums of A059484. - _N. J. A. Sloane_, Jun 02 2009
%Y Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
%K nonn
%O 0,6
%A _Vladimir Baltic_, Feb 17 2003
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