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%I #28 Mar 10 2024 16:16:49
%S 1,1,1,3,6,10,18,35,65,119,221,412,764,1416,2629,4881,9057,16807,
%T 31194,57894,107442,199399,370065,686799,1274617,2365544,4390184,
%U 8147680,15121161,28063153,52082017,96658283,179386750,332921362,617864098
%N Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=2, r=2, I={1}.
%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 Harvey P. Dale, <a href="/A080014/b080014.txt">Table of n, a(n) for n = 0..1000</a>
%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_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,-1,-1).
%F Recurrence: a(n) = a(n-1)+a(n-2)+a(n-3)+a(n-4)-a(n-5)-a(n-6).
%F G.f.: -(x^2-1)/(x^6+x^5-x^4-x^3-x^2-x+1).
%t LinearRecurrence[{1,1,1,1,-1,-1},{1,1,1,3,6,10},40] (* _Harvey P. Dale_, Mar 10 2024 *)
%o (PARI) Vec(-(x^2-1)/(x^6+x^5-x^4-x^3-x^2-x+1)+O(x^99)) \\ _Charles R Greathouse IV_, Jun 12 2015
%Y Cf. A002524-A002529, A072827, A072850..A072856, A079955..A080014.
%K nonn,easy
%O 0,4
%A _Vladimir Baltic_, Jan 24 2003
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