A347676 Array read by antidiagonals: T(n,k) (n>=1, k>=1) = number of Baxter matrices of size n X k that contain the maximal number of 1's.
1, 1, 1, 1, 4, 1, 1, 8, 8, 1, 1, 12, 26, 12, 1, 1, 16, 55, 55, 16, 1, 1, 20, 96, 156, 96, 20, 1, 1, 24, 149, 354, 354, 149, 24, 1, 1, 28, 214, 688, 1037, 688, 214, 28, 1, 1, 32, 291, 1198, 2533, 2533, 1198, 291, 32, 1, 1, 36, 380, 1924, 5383, 7632, 5383, 1924, 380, 36, 1
Offset: 1
Examples
The array begins: 1,1,1,1,1,1,1, ... 1,4,8,12,16,20,24, ... 1,8,26,55,96,149,214, ... 1,12,55,156,354,688,1198, ... 1,16,96,354,1037,2533,5383, ... 1,20,149,688,2533,7632,19522, ... 1,24,214,1198,5383,19522,59020, ... ... The first few antidiagonals are: 1, 1,1, 1,4,1, 1,8,8,1, 1,12,26,12,1, 1,16,55,55,16,1, 1,20,96,156,96,20,1, 1,24,149,354,354,149,24,1, 1,28,214,688,1037,688,214,28,1, ...
Links
- Michael S. Branicky, Table of n, a(n) for n = 1..96
- Don Knuth, Baxter matrices, Preprint, Sep 05 2021.
- George Spahn, Counting Baxter Matrices, arXiv:2110.09688 [math.CO], 2021.
Formula
a(n) <= A347672(n). - Michael S. Branicky, Sep 15 2021
Extensions
a(45)-a(66) from Michael S. Branicky, Sep 14 2021