A135707 Consider a domino formed from two adjacent 1 X 1 squares. This is the decimal expansion of the average distance between a random point in the left square and a random point in the right square.

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

Offset

1,3

Links

Table of n, a(n) for n=1..99.

Formula

(116 - 8 Sqrt[2] - 20 Sqrt[5] + 140 ArcCsch[2] - 40 ArcSinh[1] + 80 ArcSinh[2] + Log[32] + 10 Log[-1 + Sqrt[5]] - 15 Log[123 + 55 Sqrt[5]]) / 120

Example

1.0881382498612540260133800398822187615937033186594483235371...

Mathematica

d[x1_, y1_, x2_, y2_] := Sqrt[ (x1-x2)^2+(y1-y2)^2 ]
Integrate[ d[x1, y1, x2, y2], {x1, -1, 0}, {x2, 0, 1}, {y1, 0, 1}, {y2, 0, 1} ]

Crossrefs

Sequence in context: A174127 A230153 A091648 * A021923 A296496 A065465

Adjacent sequences: A135704 A135705 A135706 * A135708 A135709 A135710

Keyword

nonn,cons

Author

Richard C. Schroeppel and Michael Kleber, Mar 05 2008

Status

approved