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Search: id:A060547
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| A060547 |
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a(n) is the number of patterns, invariant under 120 degree rotations, that may appear in 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. |
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+0
5
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| 2, 1, 2, 4, 2, 4, 8, 4, 8, 16, 8, 16, 32, 16, 32, 64, 32, 64, 128, 64, 128, 256, 128, 256, 512, 256, 512, 1024, 512, 1024, 2048, 1024, 2048, 4096, 2048, 4096, 8192, 4096, 8192, 16384, 8192, 16384, 32768, 16384, 32768, 65536, 32768, 65536, 131072
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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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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)+(n mod 3)mod 2]
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MAPLE
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gf := (1+x^2+x^4)/(1-x^3)^2: s := series(gf, x, 100): for i from 0 to 70 do printf(`%d, `, 2^coeff(s, x, i)) od:
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PROGRAM
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(PARI) { for (n=1, 500, write("b060547.txt", n, " ", 2^(floor(n/3) + (n % 3) % 2)); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 07 2009]
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CROSSREFS
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a(n)=2^A008611(n-1) for n >= 1. Cf. A060550.
Sequence in context: A121339 A099500 A120253 this_sequence A079878 A137406 A120855
Adjacent sequences: A060544 A060545 A060546 this_sequence A060548 A060549 A060550
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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 03 2001
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 04 2001
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