A077865 Expansion of (1-x)^(-1)/(1-x-2*x^2+x^3).

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

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

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (2,1,-3,1)

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

Adjacent sequences: A077862 A077863 A077864 * A077866 A077867 A077868

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved