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%I #8 Jan 02 2021 14:20:08
%S 0,0,0,1,1,1,2,4,5,7,10,13,17,21,28,35,44,50,64,75,92,104,128,143,172,
%T 190,228,252,297,321,378,411,477,513,594,636,729,777,888,946,1072,
%U 1132,1280,1354,1520,1600,1792,1882,2096,2196,2440,2555,2825,2945,3250,3390,3725,3875
%N Sum of the smallest parts q 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 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))) * k.
%t Table[Sum[Sum[Sum[k*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 Cf. A062890, A340247, A340248, A340249.
%K nonn
%O 1,7
%A _Wesley Ivan Hurt_, Jan 01 2021
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