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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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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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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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