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Search: id:A060552
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| A060552 |
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a(n) is the number of distinct (modulo geometric D3-operations) nonsymmetric (no reflective nor rotational symmetry) patterns 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, 0, 0, 1, 2, 7, 14, 35, 70, 154, 310, 650, 1300, 2666, 5332, 10788, 21588, 43428, 86856, 174244, 348488, 697992, 1396040, 2794120, 5588240, 11180680, 22361360, 44730896, 89462032, 178940432, 357880864, 715794960
(list; graph; listen)
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OFFSET
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1,5
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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^(n-1)-2^[floor(n/3)+(n mod 3)mod 2-1]}/3+2^{floor[(n+3)/6]+d(n)-1} -2^floor[(n-1)/2], with d(n)=1 if n mod 6=1 else d(n)=0.
Contribution from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 03 2009: (Start)
a(n)= 2*a(n-1) +2*a(n-2) -2*a(n-3) -4*a(n-4) -4*a(n-5) +10*a(n-6) -4*a(n-7) -4*a(n-8) +4*a(n-9) +8*a(n-10) +8*a(n-11) -16*a(n-12).
G.f.: -x^4*(-1-x^2-x^4+2*x^3+2*x^5+2*x^6)/((2*x-1)*(2*x^2-1)*(2*x^3-1)*(2*x^6-1)). (End)
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PROGRAM
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(PARI) { for (n=1, 500, a=(2^(n-1)-2^(floor(n/3)+(n%3)%2-1))/3+2^(floor((n+3)/6)+(n%6==1)-1)-2^floor((n-\ 1)/2); write("b060552.txt", n, " ", a); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 07 2009]
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CROSSREFS
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A060552(n)=[A000079(n-1) - A060547(n)/2]/3 + A060548(n)/2 -A060546(n)/2 A060552(n)={A000079(n-1) - 2^[A008611(n-1)-1]}/3+ 2^[A008615(n+1)-1] -2^[A008619(n-1)-1], n >= 1
Sequence in context: A018453 A000147 A128902 this_sequence A167762 A018497 A107373
Adjacent sequences: A060549 A060550 A060551 this_sequence A060553 A060554 A060555
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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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