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A077865
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Expansion of (1-x)^(-1)/(1-x-2*x^2+x^3).
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2
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1, 2, 5, 9, 18, 32, 60, 107, 196, 351, 637, 1144, 2068, 3720, 6713, 12086, 21793, 39253, 70754, 127468, 229724, 413907, 745888, 1343979, 2421849, 4363920, 7863640, 14169632, 25532993, 46008618, 82904973, 149389217, 269190546, 485064008, 874055884, 1574993355
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OFFSET
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0,2
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COMMENTS
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a(n-1)=R(n) for n>=1, where R(n) is the number of 01-words of length n in which all runlengths of 1's are odd. Example: R(3) counts 001,010,100,101,111. - Clark Kimberling, Jun 26 2004
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REFERENCES
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Clark Kimberling, Binary words with restricted repetitions and associated compositions of integers, in Applications of Fibonacci Numbers, vol.10, Proceedings of the Eleventh International Conference on Fibonacci Numbers and Their Applications, William Webb, editor, Congressus Numerantium, Winnipeg, Manitoba 194 (2009) 141-151.
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LINKS
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Table of n, a(n) for n=0..35.
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FORMULA
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a(n)=a(n-1)+2a(n-2)-a(n-3)+1 for n>=3. a(n)=2a(n-1)+a(n-2)-3a(n-3)+a(n-4) for n>=4. - Clark Kimberling, Jun 26 2004
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PROG
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(PARI) Vec((1-x)^(-1)/(1-x-2*x^2+x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
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CROSSREFS
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Sequence in context: A091356 A107705 A002883 * A117353 A103422 A217210
Adjacent sequences: A077862 A077863 A077864 * A077866 A077867 A077868
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Nov 17 2002
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STATUS
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approved
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