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A085358 Runs of zeros in binomial(3k,k)/(2k+1) (Mod 2): relates ternary trees (A001764) to the infinite Fibonacci word (A003849). 2
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; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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,...}.

LINKS

Table of n, a(n) for n=0..92.

FORMULA

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}, ...

CROSSREFS

Cf. A001764 (ternary trees), A003849 (infinite Fibonacci word), A000975 (records), A085357.

Sequence in context: A286677 A199868 A010588 * A146104 A120235 A323411

Adjacent sequences:  A085355 A085356 A085357 * A085359 A085360 A085361

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 25 2003

STATUS

approved

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Last modified February 17 15:19 EST 2019. Contains 320220 sequences. (Running on oeis4.)