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A335701
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Irregular triangle read by rows: consider the structure formed by drawing the lines connecting any two of the 2*(n+2) perimeter points of an (n+1) X 3 rectangular grid of points (or equally, an n X 2 grid of squares); row n gives number of cells with k sides, for k >= 3.
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2
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14, 2, 48, 8, 102, 36, 4, 192, 92, 12, 326, 194, 24, 524, 336, 28, 4, 802, 554, 80, 1192, 812, 128, 4, 1634, 1314, 112, 0, 4, 2, 2296, 1756, 200, 20, 3074, 2508, 236, 22, 4052, 3252, 356, 28, 5246, 4348, 472, 28, 6740, 5464, 652, 28, 8398, 7054, 656, 74, 10440, 8760, 940, 52, 12770, 11050, 1040, 58, 15512, 13324, 1300, 60, 4, 18782, 16162, 1600, 70, 22384, 19256, 1948, 104
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OFFSET
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1,1
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COMMENTS
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More than the usual number of terms are given, in order to include the first 20 rows and emphasize the fact that so far k is never more than 8.
These are the structures discussed in column 2 of the table in A331452. It is known that the structures discussed in column 1 of that table have cells with at most 4 sides, so an upper limit of 8 sides for the present sequence is certainly possible.
The maximum number of sides for n=19..106 is 6. - Lars Blomberg, Aug 27 2020
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LINKS
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EXAMPLE
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Triangle begins:
14, 2,
48, 8,
102, 36, 4,
192, 92, 12
326, 194, 24
524, 336, 28, 4
802, 554, 80,
1192, 812, 128, 4
1634, 1314, 112, 0, 4, 2
2296, 1756, 200, 20
3074, 2508, 236, 22
4052, 3252, 356, 28
5246, 4348, 472, 28
6740, 5464, 652, 28
8398, 7054, 656, 74
10440, 8760, 940, 52
12770, 11050, 1040, 58
15512, 13324, 1300, 60, 4
18782, 16162, 1600, 70
22384, 19256, 1948, 104
...
The 1X2 structure (or 2X1 structure, as in the illustration) contains 14 triangles and 2 quadrilaterals, so row 1 is 14, 2.
The 3X2 structure contains 102 triangles, 36 quadrilaterals, and 4 pentagons, so row 3 is 102, 36, 4. The sum is 142 = A331766(3).
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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