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A126883
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a(n) = (2^0)*(2^1)*(2^2)*(2^3)...(2^n)-1 = 2^T(n) - 1 where T(n) = A000217(n) is the n-th triangular number.
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3
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0, 1, 7, 63, 1023, 32767, 2097151, 268435455, 68719476735, 35184372088831, 36028797018963967, 73786976294838206463, 302231454903657293676543, 2475880078570760549798248447, 40564819207303340847894502572031, 1329227995784915872903807060280344575
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OFFSET
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0,3
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COMMENTS
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For n > 2, a(n) and a(n-1) share at least one prime factor.
Shows how many patterns can be created with 1-color thread while sewing on a button with buttonholes located on the vertices of a convex n-gon. - Ivan N. Ianakiev, Feb 09 2012
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REFERENCES
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Masha Gessen, Perfect Rigor, A Genius and the Mathematical Breakthrough of the Century, Houghton Mifflin Harcourt, 2009, page 38.
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LINKS
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FORMULA
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MAPLE
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MATHEMATICA
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PROG
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(GAP) List([-1..15], n->2^(Binomial(2+n, n))-1); # Muniru A Asiru, Feb 21 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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