Recurrence, linear, order 02, (1,1)

This article needs more work.

Please help by expanding it!

These are the Gopala-Hemachandra sequences (generalized Fibonacci sequence of order 2)

${\{s}\}_{n=1}^{\infty }=\{{a,\ b,\ a+b,\ a+2b,\ 2a+3b,\ 3a+5b,\ 5a+8b,\ 8a+13b,\ 13a+21b,\ 21a+34b,\ ...}\},\,$

where the Fibonacci sequence correspond to (a, b) = (1, 1) and the Lucas sequence correspond to (a, b) = (1, 3.)

See also

• Fibonacci sequence
• Lucas sequence

External links

• Subhash Kak, The Golden Mean and the Physics of Aesthetics, Louisiana State University, Baton Rouge, Louisiana, 2004.
• James Harold Thomas, Variations on the Fibonacci Universal Code, Department of Electrical and Computer Engineering, Louisiana State University, Baton Rouge, Louisiana, 2007.