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

Author

Richard C. Schroeppel and Michael Kleber, Mar 05 2008

Keywords

• nonn
• cons

Examples

			1.0881382498612540260133800398822187615937033186594483235371...
		

Programs

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} ]

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