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%I #19 Jun 30 2021 06:11:11
%S 1,0,0,0,1,0,2,0,3,0,8,0,12,0,27,0,52,0,95,0,196,0,369,0,720,0,1408,0,
%T 2709,0,5292,0,10249,0,19894,0,38675,0,74992,0,145692,0,282823,0,
%U 549000,0,1066095,0,2069496,0,4018065,0,7801024,0,15144960,0,29404281,0
%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={-2,0,1,2}.
%C Also, 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,-1,0,2}. a(n)=A079980(k) 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="https://doi.org/10.2298/AADM1000008B">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_18">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1,0,4,0,2,0,2,0,-2,0,1,0,0,0,1).
%F Recurrence: a(n) = a(n-4)+4*a(n-6)+2*a(n-8)+2*a(n-10)-2*a(n-12)+a(n-14)+a(n-18).
%F G.f.: -(x^12-2*x^6+1)/(x^18+x^14-2*x^12+2*x^10+2*x^8+4*x^6+x^4-1).
%t LinearRecurrence[{0,0,0,1,0,4,0,2,0,2,0,-2,0,1,0,0,0,1},{1,0,0,0,1,0,2,0,3,0,8,0,12,0,27,0,52,0},80] (* _Harvey P. Dale_, Aug 18 2012 *)
%Y Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
%Y Bisection gives A079980 (even part).
%K nonn,easy
%O 0,7
%A _Vladimir Baltic_, Feb 17 2003
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