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A079989 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 A079989 #21 Apr 20 2023 12:12:28
%S A079989 1,1,1,1,5,13,27,51,103,221,498,1064,2240,4728,10076,21559,46075,
%T A079989 98085,208759,444727,948151,2021335,4307861,9179111,19560273,41686260,
%U A079989 88842852,189337896,403497908,859893060,1832537757,3905386173,8322891733,17737112293,37799944529
%N A079989 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 A079989 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 A079989 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 A079989 Stefano Spezia, <a href="/A079989/b079989.txt">Table of n, a(n) for n = 0..3000</a>
%H A079989 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 A079989 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,2,1,3,4,-7,-7,-6,6,-2,-1,1,4,1,-3,0,1,-1,-1).
%F A079989 a(n) = a(n-1) +a(n-2) +2*a(n-3) +a(n-4) +3*a(n-5) +4*a(n-6) -7*a(n-7) -7*a(n-8) -6*a(n-9) +6*a(n-10) -2*a(n-11) -a(n-12) +a(n-13) +4*a(n-14) +a(n-15) -3*a(n-16) +a(n-18) -a(n-19) -a(n-20).
%F A079989 G.f.: -(x^14 -x^12 +x^11 -x^9 -x^8 +x^6 -x^5 +3*x^3 +x^2-1)/( x^20 +x^19 -x^18 +3*x^16 -x^15 -4*x^14 -x^13 +x^12 +2*x^11 -6*x^10 +6*x^9 +7*x^8 +7*x^7 -4*x^6 -3*x^5 -x^4 -2*x^3 -x^2 -x +1).
%Y A079989 Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
%K A079989 nonn,easy
%O A079989 0,5
%A A079989 _Vladimir Baltic_, Feb 17 2003