A355185 Decimal expansion of the volume of the region that represents the set of points in a unit cube that are closer to the center of the cube than to the closest face.

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

Offset

-1,1

Comments

The shape is formed by the intersection of 6 paraboloids.

Links

Table of n, a(n) for n=-1..103.

Nicholas R. Baeth, Loren Luther, and Rhonda McKee, The Downtown Problem: Variations on a Putnam Problem, Mathematics Magazine, Vol. 90, No. 4 (2017), pp. 243-257.

Amiram Eldar, Illustration.

Formula

Equals (Pi + 4 - 5*sqrt(3) + (1+sqrt(3))*sqrt((2+sqrt(3))/8))/4.

Example

0.08684100488246135439728371162576930823863643930709...

Mathematica

RealDigits[(Pi + 4 - 5*Sqrt[3] + (1+Sqrt[3])*Sqrt[(2+Sqrt[3])/8])/4, 10, 100][[1]]

Crossrefs

Cf. A093066, A097047, A355183 (2D analog).

Sequence in context: A159627 A302682 A011298 * A188655 A282152 A191909

Adjacent sequences: A355182 A355183 A355184 * A355186 A355187 A355188

Keyword

nonn,cons

Author

Amiram Eldar, Jun 23 2022

Status

approved