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 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

%I

%S 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,

%T 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,

%U 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

%N 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.

%F (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

%e 1.0881382498612540260133800398822187615937033186594483235371...

%t d[x1_,y1_,x2_,y2_] := Sqrt[ (x1-x2)^2+(y1-y2)^2 ]

%t Integrate[ d[x1,y1,x2,y2], {x1,-1,0},{x2,0,1},{y1,0,1},{y2,0,1} ]

%K nonn,cons

%O 1,3

%A Richard C. Schroeppel and _Michael Kleber_, Mar 05 2008

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Last modified June 19 15:42 EDT 2021. Contains 345142 sequences. (Running on oeis4.)