A394601 - OEIS

A394601

Decimal expansion of the mean distance between two points selected independently at random within the interior of a rhombus with a unit side length and an acute angle of 60 degrees.

5, 1, 2, 3, 7, 8, 3, 3, 6, 0, 0, 0, 5, 6, 8, 0, 6, 2, 4, 1, 3, 7, 2, 1, 1, 0, 6, 8, 5, 6, 5, 4, 4, 7, 0, 3, 6, 7, 6, 2, 8, 2, 0, 4, 3, 0, 7, 6, 1, 6, 1, 1, 9, 0, 5, 4, 2, 6, 9, 4, 4, 5, 3, 7, 6, 6, 3, 0, 0, 7, 4, 6, 5, 7, 6, 3, 8, 8, 4, 5, 6, 7, 9, 0, 1, 6, 3, 9, 6, 1, 4, 9, 7, 8, 8, 3, 4, 3, 7, 3, 4, 2, 3, 0, 3

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..104.

Yanyan Zhuang and Jianping Pan, Random Distances Associated with Rhombuses, arXiv:1106.1257 [math.GM], 2011.

FORMULA

Equals sqrt(3)/8 + 3/40 + (7*log(2*sqrt(3)+3) - 6*log(2*sqrt(3)-3))/80.

EXAMPLE

0.512378336000568062413721106856544703676282043076161...

MATHEMATICA

RealDigits[Sqrt[3]/8 + 3/40 + (7*Log[2*Sqrt[3] + 3] - 6*Log[2*Sqrt[3] - 3])/80, 10, 120][[1]]

PROG

(PARI) sqrt(3)/8 + 3/40 + (7*log(2*sqrt(3)+3) - 6*log(2*sqrt(3)-3))/80

CROSSREFS

Cf. A091505 (square), A093064 (triangle), A093070 (disk), A394596 (pentagon), A394597 (hexagon), A394598 (octagon), A394599 (10-gon), A394600 (12-gon), this constant (rhombus), A394602 (rectangle).

Sequence in context: A055185 A281409 A120579 * A093316 A085758 A154529

Adjacent sequences: A394598 A394599 A394600 * A394602 A394603 A394604

KEYWORD

nonn,cons

AUTHOR

Amiram Eldar, Mar 26 2026

STATUS

approved