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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.
4
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
1,5
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
EXAMPLE
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,
...
CROSSREFS
Row 3 is A347677.
Sequence in context: A158687 A141541 A334552 * A177947 A132789 A319251
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Sep 10 2021
EXTENSIONS
a(45)-a(66) from Michael S. Branicky, Sep 14 2021
STATUS
approved