cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A120884 (1/8)*number of lattice points with odd indices in a cubic lattice inside a sphere around the origin with radius 2*n.

Original entry on oeis.org

1, 4, 17, 35, 69, 114, 184, 272, 389, 528, 702, 901, 1166, 1442, 1791, 2157, 2584, 3058, 3596, 4194, 4878, 5590, 6388, 7232, 8219, 9228, 10339, 11512, 12776, 14138, 15600, 17172, 18865, 20621, 22493, 24420, 26559, 28768, 31109, 33512, 36117, 38781
Offset: 1

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Author

Hugo Pfoertner, Jul 12 2006

Keywords

Comments

lim n->infinity a(n)/n^3 = Pi/6.

Examples

			a(2)=4 because the 4 lattice points in the first octant (x,y,z)={(1,1,1), (1,1,3), (1,3,1), (3,1,1)} all satisfy x^2+y^2+z^2 < (2*2)^2.
		

Crossrefs

A329302 Number of level-n cubes on a Menger Sponge that are enclosed in the inscribed sphere of the starting cube.

Original entry on oeis.org

0, 44, 2320, 54800, 1146112, 23278472, 468028264, 9376805048, 187644496672, 3753613318520, 75077089399408, 1501573939443704, 30031693123408792, 600635291349699440, 12012715352891236816, 240254370564131706488, 4805087834658423387496, 96101759515675744360544
Offset: 1

Views

Author

Zhao Hui Du, Nov 30 2019

Keywords

Comments

A level-n cube is understood to be enclosed in a sphere if each of its 8 vertices lies either inside or on the surface of the sphere.
This sequence is a 3D extension to A293288.

Crossrefs

Extensions

a(9)-a(18) from Ickiverar added by Zhao Hui Du, Jan 10 2020
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