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A320422
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The number of tiles inside a regular n-gon created by diagonals that run from each of the n vertices to the n-2 midpoints of opposite edges.
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3
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6, 25, 50, 145, 224, 497, 684, 1281, 1650, 2713, 3406, 5223, 6300, 9137, 10744, 14779, 17214, 23161, 26250, 34277, 38456, 49105, 54500, 68225, 75114, 92457, 101094, 122371
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OFFSET
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3,1
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COMMENTS
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Sequence proposed by Thomas Young: draw the regular n-gon and construct n*(n-2) diagonals that run from each of the n vertices to the n-2 points in the middle of the opposite edges, where opposite edges are those not adjacent to the vertex. Count the non-overlapping polygons inside the n-gon which have sides that are sections of the diagonals or sections of the n-gon edges.
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LINKS
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FORMULA
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Conjecture: a(2n+1) = n*(2*n+1)*(4*n^2-3*n+5)/3. - Thomas Young (tyoung(AT)district16.org), Jan 05 2019
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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