A264841 Triangle read by rows: T(n,k) is the number of ways to partition an n X k square grid into any number of parts along the gridlines.
1, 2, 12, 4, 74, 1442, 8, 456, 28028, 1716098, 16, 2810, 544844, 105093828, 20276816980, 32, 17316, 10591310, 6435880414, 3912156203494, 2378025136264102, 64, 106706, 205886234, 394129505248, 754801786191820, 1445496758320387318, 2768227968406304217000, 128, 657552, 4002256640, 24136256828880
Offset: 1
Examples
The triangle T(n,k) begins: n\k 1 2 3 4 5 1: 1 2: 2 12 3: 4 74 1442 4: 8 456 28028 1716098 5: 16 2810 544844 105093828 20276816980
Links
- Danny Rorabaugh, A264841 Example: T(2,2)
- R. J. Mathar, Counting 2-way monotonic terrace forms over rectangular landscapes, see Section 6.3, Combinatorics and Graph Theory, viXra:1511.0225, 2015.
Crossrefs
A078469 is the second column of this triangle.
Formula
T(n,1) = 2^(n-1).
T(n,2) = A078469(n).
Comments