A394379 a(n) is the distance between circumcenter O and centroid G of the triangle (A394102(n), A394101(n), A394100(n)).

0, 1, 5, 7, 8, 11, 16, 13, 3, 15, 21, 17, 33, 32, 39, 19, 8, 51, 40, 40, 57, 56, 23, 5, 25, 69, 35, 75, 55, 65, 88, 85, 29, 56, 95, 24, 104, 31, 87, 48, 115, 93, 96, 64, 7, 120, 35, 784, 35, 145, 37, 136, 105, 155, 77, 91, 119, 168, 133, 111, 16, 161, 41, 152, 175

Offset

1,3

Comments

On the Euler line, the centroid G divides the segment OH in the ratio 2 : 1, with OG : GH : OH = 1 : 2 : 3. Consequently, GH = 2*a(n) and OH = 3*a(n).

Links

Table of n, a(n) for n=1..65.

Wikipedia, Euler line

Example

a(1) = 0 because for the triangle (x, y, z) = (1, 1, 1) we have OG = 0.
a(2) = 1 because for the triangle (x, y, z) = (5, 7, 8) we have OG = 1.
a(3) = 5 because for the triangle (x, y, z) = (7, 8, 13) we have OG = 5.

Maple

# See Huber link in A394376.

Crossrefs

Cf. A394376, A394377, A394378.

Sequence in context: A374044 A359629 A285081 * A154370 A045251 A099497

Adjacent sequences: A394376 A394377 A394378 * A394380 A394381 A394382

Keyword

nonn

Author

Felix Huber, Mar 25 2026

Status

approved