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Search: id:A096260
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| A096260 |
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Number of different triangles, squares and rectangles created when a square piece of paper is folded n times, the first time by a diagonal of the square and after by the median of the triangle. |
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+0
3
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| 1, 3, 9, 25, 62, 205, 534, 2110, 5844, 25996, 75592, 359256, 1080592, 5314480, 16315424, 81638240, 253481024, 1279358656, 3996074112, 20256075136, 63463817472
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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After unfolding the paper, the count consists of (a) triangles whose hypotenuse is parallel to the sides of the original square, (b) triangles whose hypotenuse is diagonal to the sides of the original square, (c) rectangles whose sides are parallel to the sides of the original square, and (d) rectangles whose sides are diagonal to the sides of the original square. Note that the count for (c) is A096222(2*(Ceiling(n/2)-1)). E.g. a(5) = 205 because the counts are a=32, b=64, c=100, d=9. - T. D. Noe (noe(AT)sspectra.com), Aug 09 2004
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FORMULA
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a(n) = A096227(n) + A097405(n) + 1
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CROSSREFS
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Cf. A096222.
Cf. A096227 (triangles created), A097405 (rectangles created).
Sequence in context: A004255 A101357 A065971 this_sequence A002064 A129589 A096322
Adjacent sequences: A096257 A096258 A096259 this_sequence A096261 A096262 A096263
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KEYWORD
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nonn
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AUTHOR
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Pierre CAMI (pierrecami(AT)tele2.fr), Aug 01 2004
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EXTENSIONS
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Corrected and extended by T. D. Noe (noe(AT)sspectra.com), Aug 09 2004 and Aug 16 2004
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