A334289 Sum of the lengths of all r X s rectangles such that r < s, r + s = 2n and (s - r) | (s * r).

0, 0, 4, 6, 6, 8, 8, 22, 22, 12, 12, 68, 14, 16, 78, 62, 18, 44, 20, 104, 104, 24, 24, 234, 56, 28, 94, 140, 30, 156, 32, 158, 156, 36, 178, 326, 38, 40, 182, 372, 42, 208, 44, 212, 400, 48, 48, 638, 106, 112, 234, 248, 54, 188, 262, 496, 260, 60, 60, 1040

Offset

1,3

Links

Table of n, a(n) for n=1..60.

Formula

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

Example

a(8) = 22; 2*8 = 16 has two rectangles, 4 X 12 and 6 X 10, such that (12 - 4) | (12 * 4) = 8 | 48 and (10 - 6) | (10 * 6) = 4 | 60. The sum of the lengths of the rectangles is 12 + 10 = 22.

Mathematica

Table[Sum[(2 n - i) (1 - Ceiling[(i (2 n - i))/(2 n - 2 i)] + Floor[(i (2 n - i))/(2 n - 2 i)]), {i, n - 1}], {n, 80}]

Crossrefs

Cf. A333754.

Sequence in context: A070259 A111653 A228363 * A173395 A305317 A049089

Adjacent sequences: A334286 A334287 A334288 * A334290 A334291 A334292

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 23 2020

Status

approved