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

0,3

Links

Table of n, a(n) for n=0..55.

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.

Example

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,
...

Crossrefs

First column is A099250.

Cf. A064189.

Sequence in context: A171870 A244144 A201337 * A114263 A094850 A163973

Adjacent sequences: A291080 A291081 A291082 * A291084 A291085 A291086

Keyword

nonn,tabf

Author

N. J. A. Sloane, Aug 19 2017

Status

approved