A291082 Irregular triangle read by rows: T(n,m) = number of lattice paths of type {A^Q}_R terminating at point (n, m).

1, 2, 2, 1, 9, 12, 9, 4, 1, 51, 76, 69, 44, 20, 6, 1, 323, 512, 518, 392, 230, 104, 35, 8, 1, 2188, 3610, 3915, 3288, 2235, 1242, 560, 200, 54, 10, 1, 15511, 26324, 29964, 27016, 20240, 12804, 6853, 3080, 1143, 340, 77, 12, 1, 113634, 196938, 232323, 220584, 177177, 122694, 73710, 38376, 17199, 6552, 2079, 532, 104, 14, 1

Offset

0,2

Links

Table of n, a(n) for n=0..63.

Rezig Boualam and Moussa Ahmia, Log-concavity and strong q-log-convexity for some generalized triangular arrays, arXiv:2409.18886 [math.CO], 2024. See pp. 3,6.

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;
  2,2,1;
  9,12,9,4,1;
  51,76,69,44,20,6,1;
  323,512,518,392,230,104,35,8,1;
  2188,3610,3915,3288,2235,1242,560,200,54,10,1;
  15511,26324,29964,27016,20240,12804,6853,3080,1143,340,77,12,1;
  113634,196938,232323,220584,177177,122694,73710,38376,17199,6552,2079,532,104,14,1;
  ...

Crossrefs

First column is A026945.

Sequence in context: A128463 A136730 A175714 * A295855 A364371 A285068

Adjacent sequences: A291079 A291080 A291081 * A291083 A291084 A291085

Keyword

nonn,tabf

Author

N. J. A. Sloane, Aug 19 2017

Status

approved