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Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=1, r=5, I={0,4}.
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%I #16 Apr 16 2024 10:34:56

%S 1,0,1,1,2,2,5,5,10,13,22,30,50,70,112,163,254,375,579,862,1320,1979,

%T 3015,4536,6893,10392,15764,23800,36064,54492,82521,124748,188841,

%U 285561,432174,653642,989097,1496125,2263754,3424425,5181150,7837946

%N Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=1, r=5, I={0,4}.

%C Number of compositions (ordered partitions) of n into elements of the set {2,3,4,6}.

%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_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,1,0,1).

%F a(n) = a(n-2)+a(n-3)+a(n-4)+a(n-6).

%F G.f.: -1/(x^6+x^4+x^3+x^2-1).

%Y Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.

%K nonn,easy

%O 0,5

%A _Vladimir Baltic_, Feb 19 2003