A340249 - OEIS

%I #7 Jan 02 2021 14:24:13

%S 0,0,0,1,2,2,5,8,14,18,30,35,56,63,95,109,156,166,235,255,346,369,491,

%T 517,676,707,907,952,1200,1239,1548,1605,1974,2037,2481,2550,3078,

%U 3156,3774,3874,4592,4685,5522,5642,6596,6726,7818,7958,9200,9354,10754,10939,12510

%N Sum of the largest parts t 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))) * (n-i-j-k).

%t Table[Sum[Sum[Sum[(n - i - j - 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, A340246, A340247, A340248.

%K nonn

%O 1,5

%A _Wesley Ivan Hurt_, Jan 01 2021