%I #8 Aug 20 2015 23:21:09
%S 1,0,3,7,7,21,50,77,164,364,672,1330,2787,5474,10797,21945,43841,
%T 87031,174812,350175,698302,1397550,2798250,5591460,11181661,22374660,
%U 44740503,89467147,178965787,357927801,715796390,1431659537,2863370744,5726556304,11453194452
%N Number of set partitions of [n] into exactly four parts such that no part contains two elements with a circular distance less than three.
%H Alois P. Heinz, <a href="/A261480/b261480.txt">Table of n, a(n) for n = 4..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,5,4,-1,-4,-4).
%F G.f.: (2*x^3+2*x^2+1)*x^4/((x-1)*(2*x-1)*(x+1)*(x^2+x+1)*(2*x^2+x+1)).
%e a(4) = 1: 1|2|3|4.
%e a(6) = 3: 14|25|3|6, 14|2|36|5, 1|25|36|4.
%e a(7) = 7: 14|25|36|7, 14|25|37|6, 14|26|37|5, 15|26|37|4, 15|26|3|47, 15|2|36|47, 1|25|36|47.
%e a(8) = 7: 14|26|37|58, 14|27|36|58, 15|26|37|48, 15|26|38|47, 15|27|36|48, 16|25|37|48, 16|25|38|47.
%Y Column k=4 of A261477.
%K nonn,easy
%O 4,3
%A _Alois P. Heinz_, Aug 20 2015