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A340248 Sum of the second largest parts s of the partitions of n into 4 parts q,r,s,t such that 1 <= q <= r <= s <= t and q + r + s > t.

%I A340248 #9 Jan 02 2021 14:23:04
%S A340248 0,0,0,1,1,2,4,7,10,15,22,29,42,51,71,87,116,132,177,201,259,289,368,
%T A340248 404,508,550,681,738,900,959,1164,1239,1482,1569,1863,1962,2313,2424,
%U A340248 2835,2971,3448,3590,4150,4318,4954,5142,5872,6080,6912,7140,8078,8343,9395,9672
%N A340248 Sum of the second largest parts s of the partitions of n into 4 parts q,r,s,t such that 1 <= q <= r <= s <= t and q + r + s > t.
%F A340248 a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} sign(floor((i+k+j)/(n-i-j-k+1))) * i.
%t A340248 Table[Sum[Sum[Sum[i*Sign[Floor[(i + k + j)/(n - i - j - k + 1)]], {i, j,  Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 60}]
%Y A340248 Cf. A062890, A340246, A340247, A340249.
%K A340248 nonn
%O A340248 1,6
%A A340248 _Wesley Ivan Hurt_, Jan 01 2021