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A331939
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Triangle read by rows: Take a pentagon with all diagonals drawn, as in A331929. Then T(n,k) = number of k-sided polygons in that figure for k = 3, 4, ..., n+5.
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5
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10, 0, 1, 0, 120, 40, 10, 0, 0, 605, 290, 166, 95, 0, 5, 1750, 1420, 550, 150, 30, 0, 0, 4315, 3740, 1920, 640, 95, 20, 5, 6, 9370, 7950, 3610, 1200, 220, 20, 10, 0, 0, 17290, 15705, 7991, 2885, 520, 75, 20, 5, 0, 0, 29590, 28130, 13560, 4320, 860, 150, 0, 0, 0, 0, 0
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OFFSET
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1,1
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COMMENTS
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See the links in A331929 for images of the pentagons.
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LINKS
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EXAMPLE
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A pentagon with no other points along its edges, n = 1, contains 10 triangles, 1 pentagon and no other n-gons, so the first row is [10,0,1,0]. A pentagon with 1 point dividing its edges, n = 2, contains 120 triangles, 40 quadrilaterals, 10 pentagons and no other n-gons, so the second row is [120, 40, 10, 0, 0].
Triangle begins:
10,0,1,0
120,40,10,0,0
605,290,166,95,0,5
1750,1420,550,150,30,0,0
4315,3740,1920,640,95,20,5,6
9370,7950,3610,1200,220,20,10,0,0
17290,15705,7991,2885,520,75,20,5,0,0
29590,28130,13560,4320,860,150,0,0,0,0,0
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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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