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%I #9 Mar 31 2012 14:40:10
%S 1,0,0,0,1,3,3,3,6,10,29,39,61,101,179,335,566,928,1575,2705,4747,
%T 8117,13782,23464,40216,69209,118650,202712,346508,593180,1016874,
%U 1741871,2981190,5101520,8733466,14956519,25611753,43847283,75061015,128505176
%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={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}.
%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
%F a(n) = a(n-2) +a(n-3) +a(n-4) +4*a(n-5) +4*a(n-6) -a(n-7) -3*a(n-8) -2*a(n-9) +a(n-10) -4*a(n-11) -3*a(n-12) +a(n-13) +4*a(n-14) -a(n-16) +a(n-17) +a(n-18) -a(n-20) .
%F G.f.: -(x^14-x^12 -x^11+x^9 -2*x^8+2*x^6 +x^5+x^3 +x^2-1)/( x^20 -x^18 -x^17 +x^16 -4*x^14 -x^13 +3*x^12 +4*x^11 -x^10 +2*x^9 +3*x^8 +x^7 -4*x^6 -4*x^5 -x^4 -x^3 -x^2+1).
%Y Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
%K nonn
%O 0,6
%A _Vladimir Baltic_, Feb 17 2003
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