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%I #13 Oct 29 2017 16:42:37
%S 1,1,2,4,14,39,103,255,665,1741,4605,12046,31474,82206,215157,563083,
%T 1473635,3855111,10085589,26386595,69038554,180630858,472594580,
%U 1236463719,3235013481,8463923170,22144596592,57937977232,151585883920
%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}.
%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}.
%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
%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (1, 2, 3, 4, 6, 13, -9, -11, -7, 5, -1, -11, 3, 9, 4, -4, -1, 2, -1, -1).
%F a(n) = a(n-1) +2*a(n-2) +3*a(n-3) +4*a(n-4) +6*a(n-5) +13*a(n-6) -9*a(n-7) -11*a(n-8) -7*a(n-9) +5*a(n-10) -a(n-11) -11*a(n-12) +3*a(n-13) +9*a(n-14) +4*a(n-15) -4*a(n-16) -a(n-17) +2*a(n-18) -a(n-19) -a(n-20).
%F G.f.: -(x^14 -x^12 +x^11 -x^10 -x^9 -x^8 +3*x^6 -x^5 +x^4 +3*x^3 +x^2-1)/ (x^20 +x^19 -2*x^18 +x^17 +4*x^16 -4*x^15 -9*x^14 -3*x^13 +11*x^12 +x^11 -5*x^10 +7*x^9 +11*x^8 +9*x^7 -13*x^6 -6*x^5 -4*x^4 -3*x^3 -2*x^2 -x+1)
%t CoefficientList[Series[-(x^14-x^12+x^11-x^10-x^9-x^8+3x^6-x^5+ x^4+ 3x^3+ x^2-1)/ (x^20+ x^19-2x^18+ x^17+4x^16-4x^15-9x^14- 3x^13+ 11x^12+ x^11- 5x^10+ 7x^9+11x^8+9x^7-13x^6-6x^5-4x^4-3x^3-2x^2-x+1),{x,0,40}],x] (* or *) LinearRecurrence[{1,2,3,4,6,13,-9,-11,-7,5,-1,-11,3,9,4,-4,-1,2,-1,-1},{1,1,2,4,14,39,103,255,665,1741,4605,12046, 31474,82206,215157, 563083, 1473635,3855111,10085589,26386595},40] (* _Harvey P. Dale_, Oct 29 2017 *)
%Y Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
%K nonn
%O 0,3
%A _Vladimir Baltic_, Feb 17 2003
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