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%I #8 Dec 12 2018 03:23:02
%S 1,5,15,15,20,6,30,20,35,35,21,35,50,40,50,36,55,55,65,55,56,70,70,70,
%T 85,61,85,85,90,90,86,90,105,105,105,91,120,110,120,120,111,125,135,
%U 125,140,126,140,140,155,145,141,155,160,160,170,146,175,175,175
%N Number of compositions of n into parts with distinct multiplicities and with exactly five parts.
%H Alois P. Heinz, <a href="/A321775/b321775.txt">Table of n, a(n) for n = 5..1000</a>
%F Conjectures from _Colin Barker_, Dec 11 2018: (Start)
%F G.f.: x^5*(1 + 6*x + 21*x^2 + 35*x^3 + 49*x^4 + 34*x^5 + 29*x^6) / ((1 - x)^2*(1 + x)*(1 + x^2)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)).
%F a(n) = -a(n-1) - a(n-2) + a(n-4) + 2*a(n-5) + 2*a(n-6) + a(n-7) - a(n-9) - a(n-10) - a(n-11) for n>15.
%F (End)
%Y Column k=5 of A242887.
%K nonn
%O 5,2
%A _Alois P. Heinz_, Nov 18 2018
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