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Search: id:A085296
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| A085296 |
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Runs of zeros in Catalan sequence modulo 3: consecutive occurrences of binomial(2k,k)/(k+1) (Mod 3) = 0. |
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+0
2
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| 3, 12, 3, 39, 3, 12, 3, 120, 3, 12, 3, 39, 3, 12, 3, 363, 3, 12, 3, 39, 3, 12, 3, 120, 3, 12, 3, 39, 3, 12, 3, 1092, 3, 12, 3, 39, 3, 12, 3, 120, 3, 12, 3, 39, 3, 12, 3, 363, 3, 12, 3, 39, 3, 12, 3, 120, 3, 12, 3, 39, 3, 12, 3, 3279, 3, 12, 3, 39, 3, 12, 3, 120, 3, 12, 3, 39, 3, 12, 3
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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When we prepend a '1' to the Catalan sequence modulo 3, the only nonzero digit strings are {1,1,1,2,2,2} and {2,2,2,1,1,1}; see A085297 for the occurrences of these digit strings.
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LINKS
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R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
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FORMULA
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a(2n-1)=3, a(2n)=3*(a(n)+1), for n>=1.
a(n) = (9 * 3^A007814(n) - 1) / 2 - 1. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 10 2003
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CROSSREFS
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Cf. A000108, A039969, A085297.
Sequence in context: A162854 A110121 A069522 this_sequence A009781 A093855 A013188
Adjacent sequences: A085293 A085294 A085295 this_sequence A085297 A085298 A085299
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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 24 2003
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