cp's OEIS Frontend

A308910 Sum of the second largest parts in the partitions of n into 6 squarefree parts.

%I A308910 #9 Jun 16 2024 11:53:45
%S A308910 0,0,0,0,0,0,1,1,3,4,8,10,18,20,32,38,60,70,100,112,157,181,231,259,
%T A308910 341,382,479,531,672,743,917,1013,1253,1378,1658,1819,2205,2392,2832,
%U A308910 3065,3638,3909,4572,4890,5726,6104,7027,7495,8656,9187,10455,11130
%N A308910 Sum of the second largest parts in the partitions of n into 6 squarefree parts.
%H A308910 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308910 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 * i, where mu is the Möbius function (A008683).
%F A308910 a(n) = A308903(n) - A308906(n) - A308907(n) - A308908(n) - A308909(n) - A308911(n).
%t A308910 Table[Sum[Sum[Sum[Sum[Sum[i*MoebiusMu[i]^2*MoebiusMu[j]^2*MoebiusMu[k]^2* MoebiusMu[l]^2*MoebiusMu[m]^2*MoebiusMu[n - i - j - k - l - m]^2, {i, j, Floor[(n - j - k - l - m)/2]}], {j, k, Floor[(n - k - l - m)/3]}], {k, l, Floor[(n - l - m)/4]}], {l, m, Floor[(n - m)/5]}], {m, Floor[n/6]}], {n, 0, 50}]
%t A308910 Table[Total[Select[IntegerPartitions[n,{6}],AllTrue[#,SquareFreeQ]&][[;;,2]]],{n,0,60}] (* _Harvey P. Dale_, Jun 16 2024 *)
%Y A308910 Cf. A008683, A308902, A308903, A308906, A308907, A308908, A308909, A308911.
%K A308910 nonn
%O A308910 0,9
%A A308910 _Wesley Ivan Hurt_, Jun 29 2019