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

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• nonn
• easy

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

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

Programs

PARI

Vec((1-x)^(-1)/(1-x-2*x^2+x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

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