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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A100155 Structured truncated octahedral numbers.

Original entry on oeis.org

1, 24, 103, 272, 565, 1016, 1659, 2528, 3657, 5080, 6831, 8944, 11453, 14392, 17795, 21696, 26129, 31128, 36727, 42960, 49861, 57464, 65803, 74912, 84825, 95576, 107199, 119728, 133197, 147640, 163091, 179584, 197153, 215832, 235655, 256656, 278869, 302328
Offset: 1

Views

Author

James A. Record (james.record(AT)gmail.com), Nov 07 2004

Keywords

Links

Crossrefs

Cf. A100154, A100156 for adjacent structured Archimedean solids; A100145 for more on structured polyhedral numbers. Similar to truncated octahedral numbers A005910.

Programs

  • Magma
    [(1/6)*(34*n^3-36*n^2+8*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011
  • Mathematica
    LinearRecurrence[{4, -6, 4, -1}, {1, 24, 103, 272}, 50] (* Paolo Xausa, Aug 06 2025 *)

Formula

a(n) = (1/3)*n*(17*n^2 - 18*n + 4).
G.f.: x*(1 + 20*x + 13*x^2)/(1-x)^4. - Colin Barker, Feb 12 2012
From Elmo R. Oliveira, Aug 05 2025: (Start)
E.g.f.: exp(x)*x*(17*x^2 + 33*x + 3)/3.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4. (End)

A160247 Table read by antidiagonals of "less regular type 1" truncated octahedron numbers built from face-centered-cubic sphere packing.

Original entry on oeis.org

1, 13, 6, 55, 38, 19, 147, 116, 79, 44, 309, 260, 201, 140, 85, 561, 490, 405, 314, 225, 146, 923, 826, 711, 586, 459, 338, 231, 1415, 1288, 1139, 976, 807, 640, 483, 344
Offset: 1

Views

Author

Chris G. Spies-Rusk (chaosorder4(AT)gmail.com), May 05 2009, May 19 2009

Keywords

Comments

The sequence contains regular cuboctahedra (A005902) on the x-axis, regular octahedra (A005900) on the y-axis, and regular truncated octahedra (A005910) on the diagonal. As for the rest, they each have 6 squares of the same area, while the 8 hexagons (of another same area) have 2 side lengths which alternate.
The x-axis represents an increasing degree of truncation, while the y-axis represents an increasing quantity of units on the remaining original octahedron edge.

References

  • Main Title: Polyhedra primer / Peter Pearce and Susan Pearce. Published/Created: New York : Van Nostrand Reinhold, c1978. Description: viii, 134 p. : ill. ; 24 cm. ISBN: 0442264968
  • Main Title: The book of numbers / John H. Conway, Richard K. Guy. Published/Created: New York, NY : Copernicus c1996. Description: ix, 310 p. : ill. (some col.) ; 24 cm. ISBN: 038797993X

Programs

  • Excel
    Paste the following formula into cell C3, and fill down and right to desired table size. All volumes 10,000 and under are covered by column Q and row 27.
=(2*(ROW()-2)^3+10*(COLUMN()-2)^3+12*(ROW()-2)^2*(COLUMN()-2)+24*(ROW()-2)*(COLUMN()-2)^2-12*(ROW()-2)^2-39*(COLUMN()-2)^2-48*(ROW()-2)*(COLUMN()-2)+25*(ROW()-2)+47*(COLUMN()-2)-18)/3

Formula

v=(2*y^3+10*x^3+12*y^2x+24*Y*x^2-12*y^2-39*x^2-48*y*x+25*y+47*x-18)/3
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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