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%I A308909 #11 Jan 31 2022 16:36:01
%S A308909 0,0,0,0,0,0,1,1,2,3,6,8,14,15,23,28,39,43,62,70,98,115,152,175,227,
%T A308909 253,319,356,441,485,599,656,793,864,1026,1121,1344,1453,1709,1865,
%U A308909 2184,2357,2747,2964,3449,3719,4289,4618,5330,5693,6494,6956,7922,8430
%N A308909 Sum of the third largest parts in the partitions of n into 6 squarefree parts.
%H A308909 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308909 a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} mu(m)^2 * mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-k-j-l-m)^2 * j, where mu is the Möbius function (A008683).
%F A308909 a(n) = A308903(n) - A308906(n) - A308907(n) - A308908(n) - A308910(n) - A308911(n).
%t A308909 Table[Total[Select[IntegerPartitions[n,{6}],AllTrue[#,SquareFreeQ]&][[All,3]]],{n,0,60}] (* _Harvey P. Dale_, Jan 31 2022 *)
%Y A308909 Cf. A008683, A308902, A308903, A308906, A308907, A308908, A308910, A308911.
%K A308909 nonn
%O A308909 0,9
%A A308909 _Wesley Ivan Hurt_, Jun 29 2019

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