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.

Showing 1-7 of 7 results.

A383492 Number of polyforms with n cells on the faces of a triakis icosahedron up to rotation and reflection.

Original entry on oeis.org

1, 1, 2, 2, 4, 4, 10, 13, 29, 47, 99, 175, 358, 669, 1346, 2600, 5191, 10137, 20093, 39320, 77437, 151314, 295745, 574011, 1110144, 2130239, 4059919, 7662738, 14316799, 26413683, 48057066, 86015788, 151180505, 260256043, 437720722, 716963561, 1139830037, 1751982279, 2592522277
Offset: 0

Views

Author

Peter Kagey, Apr 28 2025

Keywords

Comments

These are "free" polyforms.
The triakis icosahedron is the polyhedral dual of the truncated dodecahedron.

Links

Crossrefs

Cf. A383493 (one-sided).
Cf. A030135 (dodecahedron), A030136 (icosahedron), A340635 (deltoidal hexecontahedron), A383490 (rhombic triacontahedron), A383494 (pentakis dodecahedron), A383496 (disdyakis triacontahedron).
Cf. A057784 (triakis triangular tiling).

Extensions

More terms from Bert Dobbelaere, Jun 10 2025

A196993 Number of fixed polypons with n cells (division into triangles is significant).

Original entry on oeis.org

6, 9, 14, 24, 42, 77, 144, 276, 538, 1065, 2136, 4321, 8790, 17967, 36890, 76050, 157380, 326824, 680880, 1422570, 2979572, 6254175, 13153242, 27712901, 58487796, 123632910, 261722022, 554800719, 1177553610, 2502256578, 5322993522
Offset: 1

Views

Author

Joseph Myers, Oct 08 2011

Keywords

Links

  • Eric Weisstein's World of Mathematics, Polypon

Crossrefs

Cf. A057784, A151531, A151532, A151533.

Extensions

a(27)-a(31) from Johann Peters, Dec 16 2024

A151531 Number of 1-sided polypons with n cells.

Original entry on oeis.org

1, 2, 3, 5, 7, 15, 24, 49, 91, 183, 356, 734, 1465, 3017, 6153, 12721, 26230, 54575, 113480, 237296, 496612, 1042785, 2192207, 4619736, 9747966, 20607348
Offset: 1

Views

Author

Ed Pegg Jr, May 13 2009

Keywords

Comments

The division of a polypon into triangles is considered significant for this sequence, as for A057784. - Joseph Myers, Oct 02 2011

Links

Crossrefs

Cf. A057784, A151532, A151533.

Extensions

a(19)-a(26) from Joseph Myers, Oct 02 2011

A151532 Number of 1-sided strip polypons with n cells.

Original entry on oeis.org

1, 2, 2, 4, 4, 7, 8, 14, 16, 26, 32, 50, 60, 93, 116, 180, 224, 340, 432, 646, 812, 1215, 1552, 2314, 2944, 4371, 5592, 8252, 10520, 15558, 19928, 29370, 37512, 55318, 70800, 104042, 132900, 195685, 250336, 367662, 469536, 690584, 882664, 1295126, 1653128, 2429594
Offset: 1

Views

Author

Ed Pegg Jr, May 13 2009

Keywords

Links

Crossrefs

Cf. A057784, A151531, A151533.

Extensions

a(21)-a(46) from Joseph Myers, Oct 02 2011

A151533 Number of 2-sided strip polypons with n cells.

Original entry on oeis.org

1, 2, 1, 3, 2, 5, 4, 9, 8, 16, 16, 28, 30, 51, 58, 96, 112, 179, 216, 334, 406, 624, 776, 1178, 1472, 2216, 2796, 4163, 5260, 7833, 9964, 14755, 18756, 27762, 35400, 52148, 66450, 98028, 125168, 184069, 234768, 345636, 441332, 647994, 826564, 1215424
Offset: 1

Views

Author

Ed Pegg Jr, May 13 2009

Keywords

Links

Crossrefs

Cf. A057784, A151531, A151532.

Extensions

a(21)-a(46) from Joseph Myers, Oct 02 2011

A355562 Number of blunt polypons with n cells.

Original entry on oeis.org

0, 1, 1, 2, 1, 5, 3, 10, 13, 31, 44, 103, 169, 360, 643, 1317, 2479, 5036, 9716, 19592, 38511, 77465, 153686, 309093, 617426, 1243392, 2496186, 5035612
Offset: 1

Views

Author

Sean A. Irvine, Jul 06 2022

Keywords

Comments

Polypons are defined in A057784. A blunt polypon is a polypon with no internal angle of 30 degrees.
Comments by Joseph Myers in A057784 regarding division of hexagons also apply to this sequence.

Links

Crossrefs

Cf. A057784, A057785 (erroneous version).

A057785 Erroneous version of A355562.

Original entry on oeis.org

0, 1, 2, 1, 1, 4, 4, 10, 13, 31, 43, 102
Offset: 1

Views

Author

N. J. A. Sloane, Nov 04 2000

Keywords

Comments

It would be nice to have a definition of "polypon"! - N. J. A. Sloane, May 09 2007
By looking at the Clarke pictures, I guess that the unit element is a triangle with internal angles of 120 degrees and two of 30 degrees. The polypons are connected, nonoverlapping assemblies of these, where connectivity is defined via common sides; a common point is not enough. Only non-congruential assemblies are counted, those which cannot be mapped onto each other by rotations, translations or mirrors along a line or point. However, the polypons are not all of these, because some of the free-form assemblies of this kind would need placement of the unit that violates the format by the grid. (The first case where this happens is with assemblies of 3 units: the picture shows 2 examples with assemblies of 3 units, but I can imagine at least 1 more where the unit would need to hide/cover one of the grid's edges.) - R. J. Mathar, Dec 10 2007

References

  • Computed by Brendan Owen.

Links

Crossrefs

Cf. A057784, A057786, A355562 (corrected version).

Extensions

Link updated by William Rex Marshall, Dec 16 2009
Showing 1-7 of 7 results.

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

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