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A327842 Number of colored integer partitions of n using all colors of a 3-set such that a color pattern for part i has i distinct colors in increasing order.

%I A327842 #6 Sep 27 2019 18:30:21
%S A327842 5,18,45,94,174,300,486,756,1131,1647,2334,3243,4416,5922,7818,10195,
%T A327842 13128,16734,21110,26403,32736,40291,49221,59748,72060,86424,103068,
%U A327842 122310,144423,169782,198711,231648,268974,311197,358761,412251,472181,539220,613959
%N A327842 Number of colored integer partitions of n using all colors of a 3-set such that a color pattern for part i has i distinct colors in increasing order.
%H A327842 Alois P. Heinz, <a href="/A327842/b327842.txt">Table of n, a(n) for n = 3..10000</a>
%H A327842 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-7,3,6,0,-6,-3,7,0,-3,1).
%F A327842 G.f.: -(x^9-6*x^7+x^6+9*x^5+3*x^4-6*x^3-9*x^2+3*x+5)*x^3 / ((x^2+x+1) *(x+1)^3 *(x-1)^7).
%Y A327842 Column k=3 of A327117.
%K A327842 nonn,easy
%O A327842 3,1
%A A327842 _Alois P. Heinz_, Sep 27 2019