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A060553
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a(n) is the number of distinct (modulo geometric D3-operations) 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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1
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2, 2, 4, 6, 10, 16, 32, 52, 104, 192, 376, 720, 1440, 2800, 5600, 11072, 22112, 43968, 87936, 175296, 350592, 700160, 1400192, 2798336, 5596672, 11188992, 22377984, 44747776, 89495040, 178973696, 357947392, 715860992
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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-1)+2^[floor(n/3) + (n mod 3)mod 2]}/3 + 2^floor[(n-1)/2]
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PROG
| (PARI) { for (n=1, 500, a=(2^(n-1) + 2^(floor(n/3) + (n%3)%2))/3 + 2^floor((n-1)/2); write("b060553.txt", n, " ", a); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 07 2009]
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CROSSREFS
| A060553(n)= [A000079(n-1) + A060547(n)]/3 + A060546(n)/2 A060553(n)= [A000079(n-1) + 2^A008611(n-1)]/3 + 2^[A008619(n-1)-1], for n >= 1
Sequence in context: A084202 A053637 A000016 * A032307 A007560 A032237
Adjacent sequences: A060550 A060551 A060552 * A060554 A060555 A060556
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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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