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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=3, r=3, I={-2,0,2}.
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%I #11 Nov 03 2015 09:35:08

%S 1,0,1,0,4,0,16,0,49,0,169,0,576,0,1936,0,6561,0,22201,0,75076,0,

%T 254016,0,859329,0,2907025,0,9834496,0,33269824,0,112550881,0,

%U 380757169,0,1288092100,0,4357584144,0,14741602225

%N Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={-2,0,2}.

%C a(n)=( A000073(k+2) )^2 if n=2k, a(n)=0 otherwise.

%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_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 2, 0, 3, 0, 6, 0, -1, 0, 0, 0, -1).

%F a(n) = 2*a(n-2)+3*a(n-4)+6*a(n-6)-a(n-8)-a(n-12).

%F G.f.: -(x^6+x^4+x^2-1)/(x^12+x^8-6*x^6-3*x^4-2*x^2+1)

%t LinearRecurrence[{0,2,0,3,0,6,0,-1,0,0,0,-1},{1,0,1,0,4,0,16,0,49,0,169,0},50] (* _Harvey P. Dale_, Nov 03 2015 *)

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

%K nonn

%O 0,5

%A _Vladimir Baltic_, Feb 17 2003