A333275 revision #20
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A333275
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Irregular triangle read by rows: consider the graph defined in A306302 formed from a row of n adjacent congruent rectangles by drawing the diagonals of all visible rectangles; T(n,k) (n >= 1, 2 <= k <= 2n+2) is the number of non-boundary vertices in the graph at which k polygons meet.
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7
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0, 0, 1, 0, 0, 6, 0, 1, 0, 0, 24, 0, 2, 0, 1, 0, 0, 54, 0, 8, 0, 2, 0, 1, 0, 0, 124, 0, 18, 0, 2, 0, 2, 0, 1
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OFFSET
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1,6
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COMMENTS
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The number of polygons meeting at a non-boundary vertex is simply the degree (or valency) of that vertex.
See A333274 for the degrees if the boundary vertices are included.
T(n,k) = 0 if k is odd. But the triangle includes those zero entries because this is used to construct A333274.
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LINKS
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EXAMPLE
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Led d denote the number of polygons meeting at a vertex.
For n=2, in the interiors of each of the two squares there are 3 points with d=4, and the center point has d=6.
So in total there are 6 points with d=4 and 1 with d=6. So row 2 of the triangle is [0, 0, 6, 0, 1].
The triangle begins:
0,0,1,
0,0,6,0,1,
0,0,24,0,2,0,1,
0,0,54,0,8,0,2,0,1,
0,0,124,0,18,0,2,0,2,0,1,
...
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CROSSREFS
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KEYWORD
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nonn,tabf,more
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AUTHOR
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STATUS
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approved
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