A332891 - OEIS

A332891

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

0, 0, 2, 2, 4, 4, 6, 10, 14, 8, 10, 28, 12, 12, 42, 34, 16, 28, 18, 56, 64, 20, 22, 102, 44, 24, 68, 84, 28, 84, 30, 98, 108, 32, 102, 178, 36, 36, 130, 188, 40, 128, 42, 140, 230, 44, 46, 322, 90, 88, 174, 168, 52, 136, 178, 288, 196, 56, 58, 520, 60, 60, 324, 258

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..64.

FORMULA

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

EXAMPLE

a(8) = 10; 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 widths of the rectangles is 4 + 6 = 10.

MATHEMATICA

Table[Sum[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: A192326 A131733 A128745 * A188524 A126064 A066813

Adjacent sequences: A332888 A332889 A332890 * A332892 A332893 A332894

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Apr 23 2020

STATUS

approved