A380392 Irregular triangle read by rows: T(n,k) is the number of n X n binary matrices containing k South-East paths of 1's connecting the top left and bottom right corners.
1, 1, 1, 13, 2, 1, 461, 26, 13, 8, 1, 2, 1, 61708, 1454, 953, 568, 325, 112, 178, 76, 22, 46, 48, 2, 16, 4, 4, 8, 8, 0, 1, 2, 1, 32348492, 340768, 279142, 168300, 125121, 44436, 81857, 24666, 25375, 28182, 19759, 4476, 17477, 4334, 7123, 6436, 4314, 1708, 5534
Offset: 0
Examples
Triangle begins:
k=0 1 2 3 4 5 6
n=0 1;
n=1 1, 1;
n=2 13, 2, 1;
n=3 461, 26, 13, 8, 1, 2, 1;
...
For row n = 3 the possible South-East paths are:
A. B. C. D. E. F.
[1 1 1] [1 1 0] [1 1 0] [1 0 0] [1 0 0] [1 0 0]
[0 0 1] [0 1 1] [0 1 0] [1 1 1] [1 1 0] [1 0 0]
[0 0 1] [0 0 1] [0 1 1] [0 0 1] [0 1 1] [1 1 1]
The 3 X 3 matrix below does not contain any of the paths A-F so it is counted under T(3,0) = 461.
[1 0 1]
[1 1 1]
[1 0 0]
The 3 X 3 matrix below contains paths A, B, and D so it is counted under T(3,3) = 8.
[1 1 1]
[1 1 1]
[1 0 1]
Links
- John Tyler Rascoe, Rows n = 0..5, flattened
- John Tyler Rascoe, Python program.
Crossrefs
Programs
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Python
# see links
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