%I #20 Apr 16 2024 04:17:31

%S 1,1,2,4,8,15,30,58,113,220,429,835,1627,3169,6173,12024,23422,45623,

%T 88869,173107,337194,656817,1279409,2492150,4854439,9455922,18419114,

%U 35878442,69887326,136132954,265172275,516526919,1006138588,1959849178

%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={4}.

%C Number of compositions (ordered partitions) of n into elements of the set {1,2,3,4,6}.

%C Note that the number of compositions of n with parts in N which avoid the pattern 221 (see Heubach/Mansour) is not this sequence but A134044.

%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 S. Heubach and T. Mansour, <a href="https://arxiv.org/abs/math/0603285">Enumeration of 3-letter patterns in combinations</a>, arXiv:math/0603285 [math.CO], 2006.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,0,1).

%F a(n) = a(n-1)+a(n-2)+a(n-3)+a(n-4)+a(n-6).

%F G.f.: -1/(x^6+x^4+x^3+x^2+x-1).

%Y Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.

%K nonn,easy

%O 0,3

%A _Vladimir Baltic_, Feb 19 2003