

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.


0



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
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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[ (x1x2)^2+(y1y2)^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



