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A056449
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a(n) = 3^floor((n+1)/2).
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11
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1, 3, 3, 9, 9, 27, 27, 81, 81, 243, 243, 729, 729, 2187, 2187, 6561, 6561, 19683, 19683, 59049, 59049, 177147, 177147, 531441, 531441, 1594323, 1594323, 4782969, 4782969, 14348907, 14348907, 43046721, 43046721, 129140163, 129140163, 387420489, 387420489, 1162261467
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OFFSET
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0,2
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COMMENTS
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One followed by powers of 3 with positive exponent, repeated. - Omar E. Pol, Jul 27 2009
Number of achiral rows of n colors using up to three colors. E.g., for a(3) = 9, the rows are AAA, ABA, ACA, BAB, BBB, BCB, CAC, CBC, and CCC. - Robert A. Russell, Nov 07 2018
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REFERENCES
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M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
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LINKS
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FORMULA
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a(n) = k^ceiling(n/2), where k = 3 is the number of possible colors. - Robert A. Russell, Nov 07 2018
E.g.f.: cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x). - Stefano Spezia, Dec 31 2022
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MATHEMATICA
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Table[3^Ceiling[n/2], {n, 0, 40}] (* or *)
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PROG
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(PARI) a(n)=3^floor((n+1)/2); \\ Joerg Arndt, Apr 23 2013
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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