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%I #20 Apr 16 2024 10:35:00
%S 1,1,2,4,7,14,27,51,98,187,357,683,1305,2494,4767,9110,17411,33276,
%T 63596,121544,232293,443954,848478,1621597,3099169,5923081,11320094,
%U 21634776,41348026,79023662,151028714,288643577,551650823,1054305916
%N Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=1, r=5, I={3}.
%C Number of compositions (ordered partitions) of n into elements of the set {1,2,3,5,6}.
%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 D. Applegate, M. LeBrun, N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.html">Dismal Arithmetic</a>, J. Int. Seq. 14 (2011) # 11.9.8.
%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 (1,1,1,0,1,1).
%F a(n) = a(n-1)+a(n-2)+a(n-3)+a(n-5)+a(n-6).
%F G.f.: -1/(x^6+x^5+x^3+x^2+x-1).
%t LinearRecurrence[{1,1,1,0,1,1},{1,1,2,4,7,14},40] (* _Harvey P. Dale_, Jun 05 2013 *)
%Y Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
%K nonn,easy
%O 0,3
%A _Vladimir Baltic_, Feb 19 2003
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