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A079980 Number of permutations of length 2n satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..2n, with k=3, r=3, I={-2,0,1,2}. There is no one such permutation of length 2n+1.

%I A079980 #16 Apr 16 2024 10:34:44
%S A079980 1,0,1,2,3,8,12,27,52,95,196,369,720,1408,2709,5292,10249,19894,38675,
%T A079980 74992,145692,282823,549000,1066095,2069496,4018065,7801024,15144960,
%U A079980 29404281,57086680,110832225,215178138,417759539,811069560,1574664364
%N A079980 Number of permutations of length 2n satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..2n, with k=3, r=3, I={-2,0,1,2}. There is no one such permutation of length 2n+1.
%H A079980 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 A079980 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,4,2,2,-2,1,0,1).
%F A079980 Recurrence: a(n) = a(n-2)+4*a(n-3)+2*a(n-4)+2*a(n-5)-2*a(n-6)+a(n-7)+a(n-9).
%F A079980 G.f.: -(x^6-2*x^3+1)/(x^9+x^7-2*x^6+2*x^5+2*x^4+4*x^3+x^2-1).
%Y A079980 Subsequence of A079981.
%K A079980 nonn,easy
%O A079980 0,4
%A A079980 _Vladimir Baltic_, Feb 17 2003