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A079990 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={-1,2}.

%I A079990 #11 Jul 30 2024 13:31:13
%S A079990 1,1,1,2,6,16,36,73,157,353,797,1776,3916,8636,19145,42504,94286,
%T A079990 208948,462907,1025863,2274069,5040891,11173063,24763854,54886846,
%U A079990 121655063,269646786,597664017,1324697483,2936135519,6507831521,14424377636
%N A079990 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={-1,2}.
%C A079990 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}.
%D A079990 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 A079990 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 A079990 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 2, 1, 4, 7, -4, -1, 1, 7, 3, -7, 2, 3, 0, -3, -2, 1, -1, -1).
%F A079990 a(n) = a(n-1) +a(n-2) +2*a(n-3) +a(n-4) +4*a(n-5) +7*a(n-6) -4*a(n-7) -a(n-8) +a(n-9) +7*a(n-10) +3*a(n-11) -7*a(n-12) +2*a(n-13) +3*a(n-14) -3*a(n-16) -2*a(n-17) +a(n-18) -a(n-19) -a(n-20).
%F A079990 G.f.: -(x^14-x^12+2*x^11-x^9+2*x^6-x^5+2*x^3+x^2-1)/(x^20 +x^19 -x^18 +2*x^17 +3*x^16 -3*x^14 -2*x^13 +7*x^12 -3*x^11 -7*x^10 -x^9 +x^8 +4*x^7 -7*x^6 -4*x^5 -x^4 -2*x^3 -x^2 -x+1)
%Y A079990 Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
%K A079990 nonn
%O A079990 0,4
%A A079990 _Vladimir Baltic_, Feb 17 2003