A291083 Irregular triangle read by rows: T(n,m) = number of lattice paths of type A^Q terminating at point (n, m).
1, 1, 4, 5, 3, 1, 21, 30, 25, 14, 5, 1, 127, 196, 189, 133, 70, 27, 7, 1, 835, 1353, 1422, 1140, 726, 369, 147, 44, 9, 1, 5798, 9713, 10813, 9438, 6765, 4037, 2002, 814, 264, 65, 11, 1, 41835, 71799, 83304, 77220, 60060, 39897, 22737, 11076, 4563, 1560, 429, 90, 13, 1
Offset: 0
Examples
Triangle begins: 1,1, 4,5,3,1, 21,30,25,14,5,1, 127,196,189,133,70,27,7,1, 835,1353,1422,1140,726,369,147,44,9,1, 5798,9713,10813,9438,6765,4037,2002,814,264,65,11,1, 41835,71799,83304,77220,60060,39897,22737,11076,4563,1560,429,90,13,1, 310572,542895,649845,630084,520455,373581,234780,129285,62127,25830,9163,2715,650,119,15,1, ...
Links
- Andrei Asinowski, Axel Bacher, Cyril Banderier, Bernhard Gittenberger, Analytic combinatorics of lattice paths with forbidden patterns, the vectorial kernel method, and generating functions for pushdown automata, Laboratoire d'Informatique de Paris Nord (LIPN 2019).
- Veronika Irvine, Lace Tessellations: A mathematical model for bobbin lace and an exhaustive combinatorial search for patterns, PhD Dissertation, University of Victoria, 2016.