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A333287
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Triangle read by rows: consider a figure made up of a row of n congruent rectangles and the diagonals of all visible rectangles; T(n,k) (1 <= k <= n) is the number of quadrilateral regions in the k-th rectangle.
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7
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0, 1, 1, 3, 8, 3, 5, 12, 12, 5, 7, 22, 32, 22, 7, 9, 28, 40, 40, 28, 9, 11, 38, 58, 74, 58, 38, 11, 13, 46, 74, 98, 98, 74, 46, 13, 15, 58, 92, 130, 152, 130, 92, 58, 15, 17, 68, 104, 150, 180, 180, 150, 104, 68, 17, 19, 82, 124, 180, 224, 254, 224, 180, 124, 82, 19
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history;
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internal format)
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OFFSET
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1,4
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COMMENTS
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This was originally based on the data in Jinyuan Wang's A324042, and then extended by Lars Blomberg.
It would be nice to have a formula for these entries. It is easy to see that the first column is 2n-3 for n>1.
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LINKS
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Lars Blomberg, Table of n, a(n) for n = 1..3240 (the first 80 rows)
Lars Blomberg, Scott R. Shannon and N. J. A. Sloane, Graphical Enumeration and Stained Glass Windows, 1: Rectangular Grids, (2021). Also arXiv:2009.07918.
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EXAMPLE
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Triangle begins:
0,
1, 1,
3, 8, 3,
5, 12, 12, 5,
7, 22, 32, 22, 7,
9, 28, 40, 40, 28, 9,
11, 38, 58, 74, 58, 38, 11,
...
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CROSSREFS
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Cf. A306302, A331452, A324042, A324043, A333286, A333288.
Sequence in context: A334503 A015136 A179450 * A360199 A360851 A117240
Adjacent sequences: A333284 A333285 A333286 * A333288 A333289 A333290
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KEYWORD
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nonn,tabl
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AUTHOR
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N. J. A. Sloane, Mar 20 2020
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EXTENSIONS
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a(29) and beyond from Lars Blomberg, Apr 23 2020
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STATUS
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approved
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