Continuants, Run Lengths, and Barry's Modified Pascal Triangle

Lukas Spiegelhofer, Jeffrey Shallit
2019 Electronic Journal of Combinatorics  
We show that the $n$'th diagonal sum of Barry's modified Pascal triangle can be described as the continuant of the run lengths of the binary representation of $n$. We also obtain an explicit description for the row sums.
doi:10.37236/7399 fatcat:dioyyb5ewnfi7bs3hpiqc3dwze