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Search: id:A097405
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| A097405 |
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Number of different rectangles created when a square sheet of paper is folded n times, the first time by one of the diagonals of the square and after by the median of the triangle. |
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+0
2
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| 0, 0, 8, 17, 108, 265, 1461, 4011, 21211, 62135, 322423, 977647, 5025263, 15510495, 79345631, 247115711, 1261100991, 3945447295, 20110344063, 63059984127, 321227980543, 1008422616575, 5135350103551, 16130465856511, 82131231439871
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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There are two types of rectangles: (1) those whose edges are parallel to the edges of the initial square and (2) those whose edges are diagonal to the edges of the initial square. These rectangles are enumerated by the p(x) and d(x) functions.
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FORMULA
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Let p(x) = x^2 (x+1)^2/4 and d(x) = (x^4 - x^2 - 6 x)/24. Then, for n>1, a(n) = -1 + p(2^ceiling(n/2-1)) + d(2^floor(n/2))
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CROSSREFS
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Cf. A096260, A096227, A096531.
Sequence in context: A008782 A097058 A134790 this_sequence A088588 A041537 A041126
Adjacent sequences: A097402 A097403 A097404 this_sequence A097406 A097407 A097408
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Aug 16 2004
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