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A287582 Number of set partitions of [n] such that all absolute differences between least elements of consecutive blocks and between consecutive elements within the blocks are not larger than three.

%I A287582 #7 May 26 2017 21:02:45
%S A287582 1,1,2,5,15,46,139,410,1189,3397,9615,27056,75838,212088,592314,
%T A287582 1652806,4609789,12853354,35832568,99884249,278414160,776016655,
%U A287582 2162929636,6028494326,16802444328,46831107603,130525521011,363794294041,1013948759937,2826024652739
%N A287582 Number of set partitions of [n] such that all absolute differences between least elements of consecutive blocks and between consecutive elements within the blocks are not larger than three.
%H A287582 Alois P. Heinz, <a href="/A287582/b287582.txt">Table of n, a(n) for n = 0..1000</a>
%H A287582 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%H A287582 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,-2,-10,11,10,-6,-7,1,2)
%F A287582 G.f.: -(2*x^9+7*x^8-6*x^6-x^5+11*x^4+x^3-3*x+1) / ((x^2+x-1) * (2*x^6 +3*x^5 -6*x^3 -3*x^2 -x+1) * (x-1)^2).
%F A287582 a(n) = A000110(n) for n <= 4.
%Y A287582 Column k=3 of A287417.
%Y A287582 Cf. A000110.
%K A287582 nonn,easy
%O A287582 0,3
%A A287582 _Alois P. Heinz_, May 26 2017