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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A056845 Number of distinct connected planar figures that can be formed from n non-overlapping diamonds.

Original entry on oeis.org

1, 2, 9, 41, 248, 1610, 11065, 78218, 563675, 4113988, 30329616, 225394071, 1686227909
Offset: 1

Views

Author

James Sellers, Aug 28 2000

Keywords

Comments

If you look at Vicher's picture of the 40 4-celled polydiamonds (link in A056844), near the middle of the picture is a polydiamond that looks like the traditional 2-D representation of a cube with an extra diamond stuck to the edge. Depending on how you orient the cube, there are actually 2 different ways to form this polydiamond, although there is no change in the perimeter shape. - Larry_Reeves(AT)intranetsolutions.com, Jun 22 2001; edited by Aaron N. Siegel, May 18 2022
Two figures are considered distinct even if their perimeter shapes are identical, provided their internal arrangements of diamonds are distinct (and not related by symmetry). This distinguishes the related sequence A056844 from A056845. The two sequences first diverge at n = 4. - Aaron N. Siegel, May 18 2022

Links

Crossrefs

Cf. A056844, A056785, A056786.

Extensions

Title clarified, a(6) corrected and a(7)-a(13) from Aaron N. Siegel, May 18 2022

A057782 Building block is trapezoid formed from 3 equilateral triangles; sequence gives number of pieces (polytraps) that can be formed from n such trapezoids.

Original entry on oeis.org

1, 9, 94, 1552, 27285, 509805, 9783124
Offset: 1

Views

Author

N. J. A. Sloane, Oct 29 2000

Keywords

Comments

Also known as "Polytriamonds" because the building block is the unique triamond (composite of three equilateral triangles joined edge-to-edge). - Aaron N. Siegel, May 23 2022

References

  • Computed by Brendan Owen.

Links

Crossrefs

Cf. A000577, A000228, A000105, A056844.

Extensions

Link updated by William Rex Marshall, Dec 16 2009
a(7) from Aaron N. Siegel, May 23 2022
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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