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Total volume of the family of rectangular prisms with dimensions p, q and p + q where p divides q, n = p + q and p < q.
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%I #4 Apr 25 2018 08:33:37

%S 0,0,6,12,20,78,42,152,234,250,110,1080,156,518,1500,1456,272,2988,

%T 342,3880,3612,1342,506,10704,3100,1898,7020,9016,812,19050,930,12640,

%U 12012,3298,13300,37476,1332,4142,18876,39600,1640,45822,1806,28600,51480,6118

%N Total volume of the family of rectangular prisms with dimensions p, q and p + q where p divides q, n = p + q and p < q.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = n * Sum_{i=1..floor((n-1)/2)} n * i * (n-i) (floor((n-i)/i) - floor((n-i-1)/i)).

%F a(n) = n * A303385(n).

%t Table[Sum[n*i (n - i) (Floor[(n - i)/i] - Floor[(n - i - 1)/i]), {i, Floor[(n - 1)/2]}], {n, 50}]

%Y Cf. A303385.

%K nonn,easy

%O 1,3

%A _Wesley Ivan Hurt_, Apr 24 2018