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%I #32 Dec 29 2023 11:40:25
%S 1,1,2,3,6,11,20,36,65,118,214,388,703,1274,2309,4185,7585,13747,
%T 24915,45156,81841,148329,268832,487232,883061,1600463,2900685,
%U 5257212,9528190,17268926,31298264,56725087,102808753,186330956,337706899
%N Expansion of g.f. 1/(1-x-x^2-x^4-x^5).
%C Number of compositions of n into elements of the set {1,2,4,5}.
%C Number of permutations (p(1),...,p(n)) of (1..n) satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=1, r=4, 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 Kassie Archer and Aaron Geary, <a href="https://arxiv.org/abs/2312.14351">Powers of permutations that avoid chains of patterns</a>, arXiv:2312.14351 [math.CO], 2023. See p. 15.
%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 4 (2010), 119-135
%H Milan Janjic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Janjic/janjic73.html">Binomial Coefficients and Enumeration of Restricted Words</a>, Journal of Integer Sequences, 2016, Vol 19, #16.7.3
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,1,1)
%F a(n) = a(n-1)+a(n-2)+a(n-4)+a(n-5).
%t CoefficientList[Series[1/(1-x-x^2-x^4-x^5),{x,0,40}],x] (* or *) LinearRecurrence[ {1,1,0,1,1},{1,1,2,3,6},40] (* _Harvey P. Dale_, Mar 16 2023 *)
%Y Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
%K nonn
%O 0,3
%A _Vladimir Baltic_, Feb 17 2003
%E Since this sequence arises in several different contexts, I made the definition as simple as possible. - _N. J. A. Sloane_, Apr 17 2011
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