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A123169 Continued fraction for sqrt(1/2)*(exp(sqrt(1/2))-1)/(exp(sqrt(1/2))+1). 1


%S 0,4,6,20,14,36,22,52,30,68,38,84,46,100,54,116,62,132,70,148,78,164,

%T 86,180,94,196,102,212,110,228,118,244,126,260,134,276,142,292,150,

%U 308,158,324,166,340,174,356,182,372,190,388,198,404,206,420,214,436,222,452

%N Continued fraction for sqrt(1/2)*(exp(sqrt(1/2))-1)/(exp(sqrt(1/2))+1).

%C This continued fraction shows exp(sqrt(1/2)) is irrational.

%D J. Borwein and D. Bailey, Mathematics by experiment, plausible reasoning in the 21st Century, A. K. Peters, p. 77

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).

%F a(1)=0, for n>=1 a(2n)=16n-12, a(2n+1)=8n-2.

%F a(n) = (3+(-1)^n)*(-3+2*n) for n>1. a(n) = 2*a(n-2)-a(n-4) for n>5. G.f.: 2*x^2*(x^3+6*x^2+3*x+2) / ((x-1)^2*(x+1)^2). - _Colin Barker_, Jun 28 2013

%p A123169:=n->(3+(-1)^n)*(-3+2*n): 0,seq(A123169(n), n=2..100); # _Wesley Ivan Hurt_, Apr 27 2017

%o (PARI) a(n)=if(n%2,max(4*n-6,0),8*n-12) \\ _Charles R Greathouse IV_, Jun 28 2013

%K nonn,easy

%O 1,2

%A _Benoit Cloitre_, Oct 02 2006

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Last modified December 11 02:30 EST 2019. Contains 329912 sequences. (Running on oeis4.)