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Search: id:A077865
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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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+0
3
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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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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 (ck6(AT)evansville.edu), Jun 26 2004
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REFERENCES
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C. Kimberling, "Binary words with restricted repetitions and associated compositions of integers," preprint.
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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 (ck6(AT)evansville.edu), Jun 26 2004
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CROSSREFS
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Sequence in context: A091356 A107705 A002883 this_sequence A117353 A103422 A097281
Adjacent sequences: A077862 A077863 A077864 this_sequence A077866 A077867 A077868
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 17 2002
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