Geodesic
Continuants, run lengths, and Barry's modified Pascal triangle
Lukas Spiegelhofer1 ; Jeffrey Shallit2
1Vienna University of Technology
2University of Waterloo
The electronic journal of combinatorics, Tome 26 (2019) no. 1
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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
Classification : 05A10, 05A19, 11A55, 11A63

Lukas Spiegelhofer  1   ; Jeffrey Shallit  2

1 Vienna University of Technology
2 University of Waterloo 
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     author = {Lukas Spiegelhofer and Jeffrey Shallit},
     title = {Continuants, run lengths, and {Barry's} modified {Pascal} triangle},
     journal = {The electronic journal of combinatorics},
     year = {2019},
     volume = {26},
     number = {1},
     doi = {10.37236/7399},
     zbl = {1409.05015},
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}
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Lukas Spiegelhofer; Jeffrey Shallit. Continuants, run lengths, and Barry's modified Pascal triangle. The electronic journal of combinatorics, Tome 26 (2019) no. 1. doi: 10.37236/7399

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