A242128 -id:A242128 - cp's OEIS frontend

A242129 Number of tiles added in each step if a centrally symmetric Penrose rhomb tiling, beginning with a central 'Sun' configuration, is successively extended in steps as defined below.

5, 5, 10, 15, 20, 25, 40, 30, 30, 45, 60, 55, 65, 55, 70, 75, 90, 75, 90

Offset: 1

Felix Fröhlich, May 05 2014

In each step, add a new tile to each free edge of the current tiling. The first step is the placement of the five central tiles.

			See illustrations in Fröhlich, 2019.

David Austin, Penrose tiles talk across miles, AMS Feature Column, August 2005.
Felix Fröhlich, Layers in the Penrose rhomb tiling with a "Sun" patch as a center of global fivefold rotational symmetry, 2019.
Wikipedia, Penrose tiling

Cf. A242128 (5-fold, Star), 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).

a(8)-a(19) from Felix Fröhlich, Jun 16 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.

A242935 Number of forced tiles in the local empire of the eight possible vertex configurations in a Penrose rhomb tiling, in the order D, J, S, Q, S5, K, S3, S4.

Original entry on oeis.org

0, 2, 5, 10, 25, 27, 43, 99

Offset: 1

Felix Fröhlich, May 27 2014

The sequence refers to Figures 3.5 - 3.11 on pp. 28-32 of Effinger-Dean's thesis. It has been decided that the numbers should be listed here in the OEIS in order of increasing size. - M. F. Hasler, Jun 04 2019

L. Effinger-Dean, The Empire Problem in Penrose Tilings, B.A. thesis, Williams college (Williamstown, MA), May 2006, Fig. 3.5 - 3.11, pp. 28-32.
Wikipedia, Penrose tiling.

Cf. A242128, A242129, A242894, A242895, A243884, A302176, A302841, A302842, A235857, A235858, A103906, A103907. - M. F. Hasler, Jun 04 2019

Terms reordered by M. F. Hasler, Jun 04 2019

cp's OEIS Frontend

A242129 Number of tiles added in each step if a centrally symmetric Penrose rhomb tiling, beginning with a central 'Sun' configuration, is successively extended in steps as defined below.

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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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A242935 Number of forced tiles in the local empire of the eight possible vertex configurations in a Penrose rhomb tiling, in the order D, J, S, Q, S5, K, S3, S4.

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