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A357058
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Number of regions in a square when n internal squares are drawn between the 4n points that divide each side into n+1 equal parts.
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9
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1, 5, 17, 37, 65, 93, 145, 181, 257, 309, 401, 457, 577, 653, 785, 869, 1025, 1109, 1297, 1413, 1601, 1725, 1937, 2041, 2305, 2453, 2705, 2861, 3137, 3289, 3601, 3765, 4089, 4293, 4625, 4801, 5185, 5405, 5769, 5993, 6401, 6605, 7057, 7309, 7737, 8013, 8465, 8673, 9217, 9477, 9993, 10309
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OFFSET
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0,2
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COMMENTS
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The even values of n that yield squares with non-simple intersections are 32, 38, 44, 50, 54, 62, 76, 90, 98, ... .
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LINKS
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Scott R. Shannon, Image for n = 5. This is the first term that forms squares with non-simple intersections.
Scott R. Shannon, Image for n = 32. This is the first term with n mod 2 = 0 that forms squares with non-simple intersections.
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FORMULA
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Conjecture: a(n) = 4*n^2 + 1 for squares that only contain simple intersections when cut by n internal squares. This is never the case for odd n >= 5.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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