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A308995 Sum of the fourth largest parts in the partitions of n into 8 parts.

%I A308995 #8 Nov 20 2024 19:17:40
%S A308995 0,0,0,0,0,0,0,0,1,1,2,3,6,9,15,22,35,48,71,97,139,185,254,334,447,
%T A308995 575,752,955,1227,1537,1939,2401,2991,3661,4500,5458,6639,7977,9607,
%U A308995 11452,13673,16176,19154,22511,26470,30906,36096,41906,48652,56171,64847
%N A308995 Sum of the fourth largest parts in the partitions of n into 8 parts.
%H A308995 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308995 a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} k.
%F A308995 a(n) = A308989(n) - A308990(n) - A308991(n) - A308992(n) - A308994(n) - A308996(n) - A308997(n) - A308998(n).
%t A308995 Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[k, {i, j, Floor[(n - j - k - l - m - o - p)/2]}], {j, k, Floor[(n - k - l - m - o - p)/3]}], {k, l, Floor[(n - l - m - o - p)/4]}], {l, m, Floor[(n - m - o - p)/5]}], {m, o, Floor[(n - o - p)/6]}], {o, p, Floor[(n - p)/7]}], {p, Floor[n/8]}], {n, 0, 50}]
%t A308995 Table[Total[IntegerPartitions[n,{8}][[;;,4]]],{n,0,60}] (* _Harvey P. Dale_, Nov 20 2024 *)
%Y A308995 Cf. A026814, A308989, A308990, A308991, A308992, A308994, A308996, A308997, A308998.
%K A308995 nonn
%O A308995 0,11
%A A308995 _Wesley Ivan Hurt_, Jul 04 2019