A242129 -id:A242129 - cp's OEIS frontend

A242128 Beginning with adding a central 'Star' configuration of a centrally symmetric Penrose rhomb tiling as the first step, number of tiles that can be added to the free edges of the current tiling.

5, 10, 15, 15, 30, 25, 30, 50, 40, 40, 50, 60, 60, 75, 75

Offset: 1

Felix Fröhlich, May 05 2014

			See illustration in Fröhlich, 2019.

Felix Fröhlich, Layers in the Penrose rhomb tiling with a "Star" patch as a center of global fivefold rotational symmetry, 2019.
Wikipedia, Penrose tiling

Cf. A242129 (5-fold, Sun), A242888 (7-fold, Star), A242889 (7-fold, Sun), A242890 (8-fold, Star), A242891 (8-fold, Sun), A242892 (9-fold, Star), A242893 (9-fold, Sun), A242894 (Kite and dart, Star), A242895 (Kite and dart, Sun).

More terms from Felix Fröhlich, Jun 20 2019

A242888 Beginning with adding a central 'Star' configuration of a centrally symmetric rhomb tiling with 7-fold symmetry, number of tiles that can be added to the free edges of the tiling.

Original entry on oeis.org

7, 14, 21, 14, 14, 28

Offset: 1

Felix Fröhlich, May 25 2014

S. Weber, Fourier transform on quasiperiodic point sets (select '7-fold' with 'shift (n-1)/2n')

Cf. A242128, A242129, A242889.

A242889 Beginning with adding a central 'Sun' configuration of a centrally symmetric rhomb tiling with 7-fold symmetry, number of tiles that can be added to the free edges of the tiling.

Original entry on oeis.org

7, 7, 7, 14, 21, 35, 28, 28, 42, 49, 63, 42, 56

Offset: 1

Felix Fröhlich, May 25 2014

S. Weber, Fourier transform on quasiperiodic point sets (select '7-fold' with 'shift 1/n')

Cf. A242128, A242129, A242888.

A242894 Beginning with a central 'Star' configuration of a Penrose 'Kite' and 'Dart' tiling with rotational symmetry as the first step, number of tiles that can be added to the free edges of the current tiling.

Original entry on oeis.org

5, 10, 10, 20, 20, 25, 35, 40, 40, 45, 45

Offset: 1

Felix Fröhlich, May 25 2014

The initial 5 corresponds to the initial "star" made from 5 "darts". Given the 5-fold symmetry, all terms are divisible by 5. See the illustration for the first 8 terms. - M. F. Hasler, Jun 04 2019

M. F. Hasler, Illustration of first 8 terms of A242894, Jun 04 2019
Cole Leahy, Image of a symmetric patch of tiles with a 'Star' at the center (from a question about drawing subregions of Penrose tilings on TeX - LaTeX Stack Exchange), May 2013.

Cf. A242128, A242129, A242888, A242889, A242890, A242891, A242892, A242893, A242895.

A242895 Beginning with a central 'Sun' configuration of a Penrose 'Kite' and 'Dart' tiling with rotational symmetry as the first step, number of tiles that can be added to the free edges of the current tiling.

Original entry on oeis.org

5, 5, 10, 15, 20, 25, 30

Offset: 1

Felix Fröhlich, May 25 2014

The initial 5 corresponds to the "Sun" configuration made of 5 Penrose "Kites". In view of the 5-fold rotational symmetry, all terms are divisible by 5, see the illustrations given as LINKS. - M. F. Hasler, Jun 05 2019

Sam T. Benge(?), Image of 'Sun' and 'Star' configurations in a centrally symmetric 'Kite' and 'Dart' tiling, post to the POV-Ray Newsgroup, Oct 31 2009.
Wikipedia, Penrose tiling, Deflation for P2 and P3 tilings. (Defines "sun" and "star" configurations and generations corresponding to terms of this sequence.)

Cf. A242128, A242129, A242888, A242889, A242890, A242891, A242892, A242893, A242894.

A242890 Beginning with a central 'Star' configuration of a centrally symmetric arrangement of 8 rhombi with 8-fold rotational symmetry, number of tiles that can be added to the free edges of the tiling.

Original entry on oeis.org

8, 16, 16, 16, 16, 16, 24

Offset: 1

Felix Fröhlich, May 25 2014

S. Weber, Fourier transform on quasiperiodic point sets (select '8-fold' with 'shift (n-1)/2n')

Cf. A242128, A242129, A242888, A242889, A242891, A242892, A242893, A242894, A242895.

A242891 Beginning with a centrally symmetric 'Sun' configuration of 8 rhombi with rotational symmetry, number of tiles that can be added to the free edges of the tiling.

Original entry on oeis.org

8, 8, 8, 16, 24, 24, 40, 32, 48, 48, 40

Offset: 1

Felix Fröhlich, May 25 2014

S. Weber, Fourier transform on quasiperiodic point sets (select '8-fold' with 'shift 1/n')

Cf. A242128, A242129, A242888, A242889, A242890, A242892, A242893, A242894, A242895.

A242892 Beginning with a centrally symmetric 'Star' configuration of 9 rhombi with rotational symmetry, number of tiles that can be added to the free edges of the tiling.

Original entry on oeis.org

9, 9, 18, 27, 27, 18

Offset: 1

Felix Fröhlich, May 25 2014

S. Weber, Fourier transform on quasiperiodic point sets (select '9-fold' with 'shift (n-1)/(2n)')

Cf. A242128, A242129, A242888, A242889, A242890, A242891, A242893, A242894, A242895.

A242893 Beginning with a centrally symmetric 'Sun' configuration of 9 rhombi with rotational symmetry, number of tiles that can be added to the free edges of the tiling.

Original entry on oeis.org

9, 9, 9, 9, 18, 27, 27, 36

Offset: 1

Felix Fröhlich, May 25 2014

S. Weber, Fourier transform on quasiperiodic point sets (select '9-fold' with 'shift 1/n')

Cf. A242128, A242129, A242888, A242889, A242890, A242891, A242892, A242894, A242895.

A243884 Type of walk that occurs when walking along a ray emanating from the center of a rotationally symmetric Penrose rhomb tiling with a "Sun" patch at the center (see comments for details).

Original entry on oeis.org

1, 2, 1, 2, 3, 1, 2, 4, 1, 2, 1, 2, 3, 1, 2, 1, 4, 2, 1, 3, 2, 1, 2, 1, 2, 3, 1, 2, 4, 1, 2, 1, 3, 2, 1, 2, 1, 2, 3, 1, 2, 4, 1, 2, 1, 2, 3, 1, 2, 1, 4, 2, 1, 3, 2, 1, 2, 1, 2, 3

Offset: 1

Felix Fröhlich, Jun 13 2014

The ray starts at the center of the tiling and goes through the center of one of the thick rhombs of the central "Sun" patch. The walk types that can occur are encoded as follows:
Walk type                     | Number
---------------------------------------
along diagonal of thick rhomb | 1
along edge of thick rhomb     | 2
along diagonal of thin rhomb  | 3
along edge of thin rhomb      | 4

			See illustration in Fröhlich, 2019.

Felix Fröhlich, Ray emanating from the center of a Penrose rhomb tiling with a "Sun" patch at the center, 2019.
Wikipedia, Penrose tiling

Cf. A242129.

More terms, new name and editing from Felix Fröhlich, Jun 16 2019

cp's OEIS Frontend

A242128 Beginning with adding a central 'Star' configuration of a centrally symmetric Penrose rhomb tiling as the first step, number of tiles that can be added to the free edges of the current tiling.

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A242888 Beginning with adding a central 'Star' configuration of a centrally symmetric rhomb tiling with 7-fold symmetry, number of tiles that can be added to the free edges of the tiling.

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A242889 Beginning with adding a central 'Sun' configuration of a centrally symmetric rhomb tiling with 7-fold symmetry, number of tiles that can be added to the free edges of the tiling.

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A242894 Beginning with a central 'Star' configuration of a Penrose 'Kite' and 'Dart' tiling with rotational symmetry as the first step, number of tiles that can be added to the free edges of the current tiling.

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A242895 Beginning with a central 'Sun' configuration of a Penrose 'Kite' and 'Dart' tiling with rotational symmetry as the first step, number of tiles that can be added to the free edges of the current tiling.

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A242890 Beginning with a central 'Star' configuration of a centrally symmetric arrangement of 8 rhombi with 8-fold rotational symmetry, number of tiles that can be added to the free edges of the tiling.

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A242891 Beginning with a centrally symmetric 'Sun' configuration of 8 rhombi with rotational symmetry, number of tiles that can be added to the free edges of the tiling.

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A242892 Beginning with a centrally symmetric 'Star' configuration of 9 rhombi with rotational symmetry, number of tiles that can be added to the free edges of the tiling.

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A242893 Beginning with a centrally symmetric 'Sun' configuration of 9 rhombi with rotational symmetry, number of tiles that can be added to the free edges of the tiling.

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A243884 Type of walk that occurs when walking along a ray emanating from the center of a rotationally symmetric Penrose rhomb tiling with a "Sun" patch at the center (see comments for details).

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Extensions