%I #22 Mar 21 2017 11:06:45
%S 1,1,2,4,8,14,26,48,89,163,300,552,1016,1868,3436,6320,11625,21381,
%T 39326,72332,133040,244698,450070,827808,1522577,2800455,5150840,
%U 9473872,17425168,32049880,58948920,108423968,199422769,366795657,674642394,1240860820,2282298872,4197802086,7720961778
%N Expansion of 1/(1-x-x^2-x^3-x^4+x^5+x^6+x^7).
%C This sequence counts partially ordered partitions of (n) into parts (1,2,3,4) in which the position (order) of the 4's are unimportant. For example the permutations of (43421) are counted as permutations of (321)=6.
%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,-1,-1,-1).
%F a(n)= a(n-1) + a(n-2) + a(n-3) + a(n-4) - a(n-5) - a(n-6) - a(n-7).
%F G.f.: 1 / ((x-1)*(x+1)*(x^2+1)*(x^3+x^2+x-1)). - _Colin Barker_, May 17 2015
%e a(6)=26; these are (42=24),(411=141=114),(33),(321=six),(3111=four),(222),(2211=six),(21111=five),(111111).
%o (PARI) Vec(1 / ((x-1)*(x+1)*(x^2+1)*(x^3+x^2+x-1)) + O(x^100)) \\ _Colin Barker_, May 17 2015
%Y Cf. A258000, A257863.
%K nonn,easy
%O 0,3
%A _David Neil McGrath_, May 13 2015
%E Missing term (6320) inserted by _Colin Barker_, May 17 2015