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A060551
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a(n) is the number of nonsymmetric patterns (no reflective, nor rotational symmetry) which may 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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1
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0, 0, 0, 6, 12, 42, 84, 210, 420, 924, 1860, 3900, 7800, 15996, 31992, 64728, 129528, 260568, 521136, 1045464, 2090928, 4187952, 8376240, 16764720, 33529440, 67084080, 134168160, 268385376, 536772192, 1073642592, 2147285184
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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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^n-3*2^ceil(n/2)-2^[floor(n/3)+(n mod 3)mod 2]+3*2^{floor[(n+3)/6]+d(n)}, with d(n)=1 if n mod 6=1 else d(n)=0.
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PROG
| (PARI) { for (n=1, 500, a=2^n-3*2^ceil(n/2)-2^(floor(n/3)+(n%3)%2)+3*2^(floor((n+3)/6)+(n%6==1)); write("b060551.txt", n, " ", a); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 07 2009]
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CROSSREFS
| A060551(n)=A000079(n)-3*A060546(n)-A060547(n)+3*A060548(n) A060551(n)=A000079(n)-3*2^A008619(n-1)-2^A008611(n-1)+3*2^A008615(n+1), for n >= 1
Sequence in context: A206039 A048069 A152787 * A129113 A048025 A120471
Adjacent sequences: A060548 A060549 A060550 * A060552 A060553 A060554
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KEYWORD
| easy,nonn
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AUTHOR
| Andr\'{e} Barb\'{e} (Andre.Barbe(AT)esat.kuleuven.ac.be), Apr 03 2001
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