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Search: id:A060549
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| A060549 |
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a(n) is the number of distinct patterns (modulo geometric D3-operations) with strict median-reflective (palindrome) symmetry (i.e. having no other symmetry) which can be formed by an 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
1
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| 0, 1, 2, 2, 6, 6, 12, 14, 28, 28, 60, 60, 120, 124, 248, 248, 504, 504, 1008, 1016, 2032, 2032, 4080, 4080, 8160, 8176, 16352, 16352, 32736, 32736, 65472, 65504, 131008, 131008, 262080, 262080, 524160, 524224, 1048448, 1048448, 2097024, 2097024
(list; graph; listen)
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OFFSET
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1,3
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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^ceil(n/2)-2^{floor[(n+3)/6]+d(n)}, with d(n)=1 if n mod 6=1 else d(n)=0
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PROGRAM
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(PARI) { for (n=1, 500, write("b060549.txt", n, " ", 2^ceil(n/2) - 2^(floor((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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A060549(n)=A060546(n)-A060548(n)=2^A008619(n-1)-2^A008615(n+1), for n >= 1
Sequence in context: A051548 A110660 A139550 this_sequence A120690 A165124 A056453
Adjacent sequences: A060546 A060547 A060548 this_sequence A060550 A060551 A060552
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KEYWORD
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easy,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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