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Search: id:A085358
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| A085358 |
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Runs of zeros in binomial(3k,k)/(2k+1) (Mod 2): relates ternary trees (A001764) to the infinite Fibonacci word (A003849). |
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2
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| 1, 2, 5, 1, 10, 1, 2, 21, 1, 2, 5, 1, 42, 1, 2, 5, 1, 10, 1, 2, 85, 1, 2, 5, 1, 10, 1, 2, 21, 1, 2, 5, 1, 170, 1, 2, 5, 1, 10, 1, 2, 21, 1, 2, 5, 1, 42, 1, 2, 5, 1, 10, 1, 2, 341, 1, 2, 5, 1, 10, 1, 2, 21, 1, 2, 5, 1, 42, 1, 2, 5, 1, 10, 1, 2, 85, 1, 2, 5, 1, 10, 1, 2, 21, 1, 2, 5, 1, 682, 1, 2, 5, 1
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Has complementary parity to the infinite Fibonacci word: a(n) = 1 - A003849(n) (Mod 2). Records are given by A000975, and occur at Fibonacci numbers: {1,2,5,10,21,42,85,...} occur at {1,2,3,5,8,13,21,...}.
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FORMULA
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Construction: start with strings S(1)={1} and S(2)={1, 2}; for k>2, let L=largest number in current string S(k); to obtain S(k+1), append S(k-1) to the end of S(k) and then replace the last number in this resulting string with {2L+1 (k odd) or 2L (k even)}. String lengths have Fibonacci growth: {1}, {1, 2}, {1, 2, 5}, {1, 2, 5, 1, 10}, {1, 2, 5, 1, 10, 1, 2, 21}, ...
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CROSSREFS
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Cf. A001764 (ternary trees), A003849 (infinite Fibonacci word), A000975 (records), A085357.
Sequence in context: A124576 A021401 A010588 this_sequence A120235 A089618 A101920
Adjacent sequences: A085355 A085356 A085357 this_sequence A085359 A085360 A085361
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jun 25 2003
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