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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
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
1,2
COMMENTS
A set of edges forms a valid partition if and only if it includes the entire boundary of the grid, and there are no vertices of degree 1.
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.
FORMULA
T(n,1) = 2^(n-1).
T(n,2) = A078469(n).
EXAMPLE
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
CROSSREFS
A078469 is the second column of this triangle.
Sequence in context: A066700 A159323 A038218 * A191249 A333544 A005760
KEYWORD
nonn,tabl
AUTHOR
Linus Hamilton, Nov 26 2015
STATUS
approved