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A060547
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a(n) = 2^(floor(n/3) + ((n mod 3) mod 2)).
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7
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2, 1, 2, 4, 2, 4, 8, 4, 8, 16, 8, 16, 32, 16, 32, 64, 32, 64, 128, 64, 128, 256, 128, 256, 512, 256, 512, 1024, 512, 1024, 2048, 1024, 2048, 4096, 2048, 4096, 8192, 4096, 8192, 16384, 8192, 16384, 32768, 16384, 32768, 65536, 32768, 65536, 131072
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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a(n) is the number of patterns, invariant under 120-degree rotations, that may appear 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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LINKS
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FORMULA
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MAPLE
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gf := (1+x^2+x^4)/(1-x^3)^2: s := series(gf, x, 100):
for i from 0 to 70 do printf(`%d, `, 2^coeff(s, x, i)) od:
# Alternative:
a := n -> 2^(iquo(n, 3) + irem(irem(n, 3), 2));
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MATHEMATICA
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PROG
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(PARI) { for (n=1, 500, write("b060547.txt", n, " ", 2^(floor(n/3) + (n % 3) % 2)); ) } \\ Harry J. Smith, Jul 07 2009
(Haskell)
a060547 = (2 ^) . a008611 . (subtract 1)
a060547_list = f [2, 1, 2] where f xs = xs ++ f (map (* 2) xs)
def a_gen():
a, b, c = 1, 2, 4
yield b
while True:
yield a
a, b, c = b, c, a + a
a = a_gen()
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CROSSREFS
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KEYWORD
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easy,nice,nonn
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AUTHOR
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André Barbé (Andre.Barbe(AT)esat.kuleuven.ac.be), Apr 03 2001
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EXTENSIONS
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STATUS
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approved
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