A340247 - OEIS

%I #8 Jan 02 2021 14:22:18

%S 0,0,0,1,1,1,3,5,7,10,15,19,28,33,46,57,75,84,113,129,164,184,232,256,

%T 319,347,425,466,561,601,723,777,918,981,1152,1224,1428,1509,1746,

%U 1849,2122,2227,2550,2678,3040,3184,3600,3760,4234,4410,4942,5151,5745,5961,6635

%N Sum of the third largest parts r 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))) * j.

%t Table[Sum[Sum[Sum[j*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, A340246, A340248, A340249.

%K nonn

%O 1,7

%A _Wesley Ivan Hurt_, Jan 01 2021