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Search: id:A060548
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| A060548 |
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a(n) is the number of D3-symmetric patterns that may be formed with a top-down equilateral triangular arrangement of closely packed black and white cells satisfying the local matching rule of Pascal's triangle modulo 2, where n is the number of cells in each edge of the arrangement. The matching rule is such that any elementary top-down triangle of three neighboring cells in the arrangement contains either one or three white cells. |
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+0
5
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| 2, 1, 2, 2, 2, 2, 4, 2, 4, 4, 4, 4, 8, 4, 8, 8, 8, 8, 16, 8, 16, 16, 16, 16, 32, 16, 32, 32, 32, 32, 64, 32, 64, 64, 64, 64, 128, 64, 128, 128, 128, 128, 256, 128, 256, 256, 256, 256, 512, 256, 512, 512, 512, 512, 1024, 512, 1024, 1024, 1024, 1024, 2048, 1024, 2048
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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A. Barb\'{e}, Symmetric patterns in the cellular automaton that generates Pascal's triangle modulo 2, Discr.Appl.Math. 105(2000),1-38.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,500
Index entries for sequences related to cellular automata
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FORMULA
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a(n)=2^{floor[(n+3)/6]+d(n)}, with d(n)=1 if n mod 6=1, else d(n)=0
a(n)=a(n-2)a(n-3)/a(n-5), n>5.
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PROGRAM
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(PARI) a(n)=if(n<1, 0, 2^((n+3)\6+(n%6==1)))
(PARI) { for (n=1, 500, write("b060548.txt", n, " ", 2^((n + 3)\6 + (n%6==1))); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 07 2009]
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CROSSREFS
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a(n)=2^A008615(n+1)=2^floor[A008611(n+2)/2] for n >= 1
Sequence in context: A062610 A025801 A140426 this_sequence A146879 A058762 A029252
Adjacent sequences: A060545 A060546 A060547 this_sequence A060549 A060550 A060551
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Andr\'{e} Barb\'{e} (Andre.Barbe(AT)esat.kuleuven.ac.be), Apr 02 2001
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