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Search: id:A092434
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| A092434 |
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Number of words X=x(1)x(2)x(3)...x(n) of length n in three digits {0,1,2} that are invariant under the mapping X -> Y, where y(i)=((AD)^(i-1))x(1) and where (AD) denotes the absolute difference (AD)x(i)=abs(x(i+1)-x(i)) (in other words, y(i) is the i-th element in the diagonal of leading entries in the table of absolute differences of {x(1), x(2),...,x(n)). |
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+0
1
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| 3, 4, 10, 12, 28, 32, 72, 80, 176, 192, 416, 448, 960, 1024
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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In the two digits {0,1} the corresponding sequence is 2,2,4,4,8,8,16,16,32,32,64,64,... which appears to be A060546.
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FORMULA
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It is conjectured that a(n)=(n+2)*2^((n-1) div 2).
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EXAMPLE
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The table of absolute differences of {2,1,1,0} is
2
1.1
1.0.1
0.1.1.0
with the diagonal of leading absolute differences again forming the word (2110).
Thus (2110) is one of the twelve words in the digits {0,1,2} that are counted in calculating a(4).
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CROSSREFS
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Cf. A060546.
Sequence in context: A135116 A050187 A101506 this_sequence A031367 A073443 A092119
Adjacent sequences: A092431 A092432 A092433 this_sequence A092435 A092436 A092437
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Mar 23 2004
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