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A077865 Expansion of (1-x)^(-1)/(1-x-2*x^2+x^3). 2
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; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
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
REFERENCES
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.
LINKS
FORMULA
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
PROG
(PARI) Vec((1-x)^(-1)/(1-x-2*x^2+x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
Sequence in context: A002883 A295724 A342208 * A117353 A103422 A217210
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 17 2002
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)