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#19 by Bruno Berselli at Fri Aug 26 12:22:54 EDT 2016
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#18 by Michel Marcus at Fri Aug 26 11:38:15 EDT 2016
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#17 by G. C. Greubel at Mon Aug 15 10:58:16 EDT 2016
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#16 by G. C. Greubel at Mon Aug 15 10:58:03 EDT 2016
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G. C. Greubel, <a href="/A103943/b103943.txt">Table of n, a(n) for n = 1..1000</a>
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proposed
editing
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#15 by Benedict W. J. Irwin at Sat Aug 13 14:09:32 EDT 2016
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#14 by Benedict W. J. Irwin at Sat Aug 13 14:08:04 EDT 2016
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G.f.: 1/8*(2/q^2 -2 + 1/p - 1/q + 2*sqrt(p^2-2*x)/sqrt(q^2+2*x) - sqrt(2 + 2*p*q)/(p*q)), where p=sqrt(1+4x4*x) and q=sqrt(1-4x4*x). - Benedict W. J. Irwin, Aug 13 2016
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#13 by Benedict W. J. Irwin at Sat Aug 13 14:05:11 EDT 2016
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G.f.: 1/8*(2/q^2 -2 + 1/p - 1/q + 2*sqrt(p^2-2*x)/sqrt(q^2+2*x) - sqrt(2)*sqrt(1 + 2*p*q)/(p*q)), where p=sqrt(1+4x) and q=sqrt(1-4x). - Benedict W. J. Irwin, Aug 13 2016
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#12 by Benedict W. J. Irwin at Sat Aug 13 14:02:33 EDT 2016
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G.f.: 1/8*(2/q^2 -2 + 1/p - 1/q + 2*sqrt(p^2-2*x)/sqrt(q^2+2*x) - sqrt(2)*sqrt(1 + p*q)/(p*q)), where p=sqrt(1+4x) and q=sqrt(1-4x). - Benedict W. J. Irwin, Aug 13 2016
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Rest[CoefficientList[Series[1/8(-2+2/(1-4x)-1/Sqrt[1-4x]+1/Sqrt[1+4x]+2/Sqrt[-1+2/(1+2x)]-Sqrt[1+Sqrt[1-16x^2]]/Sqrt[1/2-8x^2]), {x, 0, 20}], x]] (* Benedict W. J. Irwin, Aug 13 2016 *)
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approved
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#11 by Jon E. Schoenfield at Thu Jul 30 21:51:22 EDT 2015
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#10 by Jon E. Schoenfield at Thu Jul 30 21:51:20 EDT 2015
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2a(n)=) = 2^(2n-1)-) - binomial(2n-1, n-1)+) + binomial(n-1, floor(n/2)).
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f[n_] := (2^(2n - 1) - Binomial[2n - 1, n - 1] + Binomial[n - 1, Floor[n/2]])/2; Table[ f[n], {n, 24}] (from _}] (* _Robert G. Wilson v_, Mar 24 2005) *)
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approved
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