A072042 -id:A072042 - cp's OEIS frontend

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;

A235858 Associated with random Penrose-Robinson tilings of the plane.

Original entry on oeis.org

1, 4, 88, 236544, 211790340292608, 56686233255830734129089579999779880960

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, A235857.

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;

A126023 a(0)=0, a(1)=1; for n>1, a(n) = a(n-1)*(a(n-1)+a(n-2)).

Original entry on oeis.org

0, 1, 1, 2, 6, 48, 2592, 6842880, 46842743439360, 2194242933464976548324966400, 4814702051061088283920560140388303599459408453566464000, 23181355840491850372772514246989811472332466216882815765831029699284672633019505150499832539732598430105600000

Offset: 0

Franklin T. Adams-Watters, Feb 27 2007

Steven R. Finch, Substitution dynamics, January 23, 2014. [Cached copy, with permission of the author]
Index entries for sequences of form a(n+1)=a(n)^2 + ...

Cf. A064183.

a=0;b=1;lst={a,b};Do[c=(a+b)*b;AppendTo[lst,c];a=b;b=c,{n,2*3!}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 05 2009 *)
RecurrenceTable[{a[0]==0, a[1]==1, a[n] == a[n-1]*(a[n-1]+a[n-2])}, a, {n, 0, 10}] (* Vaclav Kotesovec, Dec 18 2014 *)

a=0;b=1;vector(11,i,c=b*(b+a);a=b;b=c;a)

a(n) ~ c^(2^n), where c = 1.130839439573188327984771046199629891088102083459871373699856783789557668... . - Vaclav Kotesovec, Dec 18 2014

cp's OEIS Frontend

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

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A235858 Associated with random Penrose-Robinson tilings of the plane.

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Author

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Comments

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Mathematica

A126023 a(0)=0, a(1)=1; for n>1, a(n) = a(n-1)*(a(n-1)+a(n-2)).

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