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A060546
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a(n) is the number of median-reflective (palindrome) symmetric patterns 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. 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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8
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2, 2, 4, 4, 8, 8, 16, 16, 32, 32, 64, 64, 128, 128, 256, 256, 512, 512, 1024, 1024, 2048, 2048, 4096, 4096, 8192, 8192, 16384, 16384, 32768, 32768, 65536, 65536, 131072, 131072, 262144, 262144, 524288, 524288, 1048576, 1048576, 2097152, 2097152
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The number of possibilities for an n-game (sub)set of tennis with neither player gaining a 2-game advantage. (Motivated by the marathon Isner-Mahut match at Wimbledon, 2010.) [From Barry Cipra (bcipra(AT)rconnect.com), Jun 28 2010]
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REFERENCES
| 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
| 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
| a(n) =2^ceil(n/2)
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MAPLE
| for n from 1 to 100 do printf(`%d, `, 2^ceil(n/2)) od:
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PROG
| (PARI) { for (n=1, 500, write("b060546.txt", n, " ", 2^ceil(n/2)); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 06 2009]
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CROSSREFS
| a(n)=A016116(n+1) for n >= 1 a(n)=2^A008619(n-1) for n >= 1
Sequence in context: A152166 A016116 * A163403 A183565 A120803 A000011
Adjacent sequences: A060543 A060544 A060545 * A060547 A060548 A060549
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KEYWORD
| easy,nice,nonn
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AUTHOR
| Andr\'{e} Barb\'{e} (Andre.Barbe(AT)esat.kuleuven.ac.be), Apr 03 2001
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 04 2001
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