A235858 -id:A235858 - cp's OEIS frontend

A072042 a(n+2) = a(n+1)a(n)(1+1/n), a(1)=a(2)=1.

1, 1, 2, 3, 8, 30, 288, 10080, 3317760, 37623398400, 138694895861760000, 5739990655358858585702400000, 868480806755424464755519466250436608000000000

Offset: 1

Benoit Cloitre, Jul 29 2002

Steven R. Finch, Substitution dynamics, January 23, 2014. [Cached copy, with permission of the author]
C. Godrèche and J. M. Luck, Quasiperiodicity and randomness in tilings of the plane, J. Statist. Phys. 55 (1989) 1-28.
J. Nilsson, On the entropy of random Fibonacci words, arXiv:1001.3513 [math.CO], 2010.

Cf. A235857, A235858.

a[1] = a[2] = 1; a[n_] := a[n - 1]*a[n - 2]*(1 + 1/(n - 2)); Table[ a[n], {n, 1, 13}]
RecurrenceTable[{a[1]==a[2]==1,a[n+2]==a[n+1]*a[n]*(1+1/n)},a,{n,13}] (* Harvey P. Dale, Sep 18 2018 *)

Edited by Robert G. Wilson v, Jul 31 2002

A235857 Associated with random Penrose-Robinson tilings of the plane.

Original entry on oeis.org

1, 2, 12, 1536, 519045120, 156130677884314787512320, 12538151702000091464104493325082133822247601116646227522355200

Offset: 0

Steven Finch, Jan 16 2014

nonn

In the Mathematica code, let p=A235857; q=A235858 for convenience.

Steven R. Finch, Substitution dynamics, January 23, 2014. [Cached copy, with permission of the author]
C. Godrèche and J. M. Luck, Quasiperiodicity and randomness in tilings of the plane, J. Statist. Phys. 55 (1989) 1-28.

Cf. A072042, A235858.

p[n_] := p[n] = 2 p[n-1] q[n-1] - p[n-1]^2 q[n-2];
q[n_] := 2 p[n] q[n-1] - p[n-1] p[n-2] q[n-1] q[n-2]^2;
p[0] = 1; q[0] = 1; p[1] = 2; q[1] = 4;

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

A072042 a(n+2) = a(n+1)a(n)(1+1/n), a(1)=a(2)=1.

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A235857 Associated with random Penrose-Robinson tilings of the plane.

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Mathematica

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.

Views

Author

Keywords

Comments

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cp's OEIS Frontend

A072042 a(n+2) = a(n+1)*a(n)*(1+1/n), a(1)=a(2)=1.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

A235857 Associated with random Penrose-Robinson tilings of the plane.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

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.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

A072042 a(n+2) = a(n+1)a(n)(1+1/n), a(1)=a(2)=1.