%I
%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)=16n12, a(2n+1)=8n2.
%F a(n) = (3+(1)^n)*(3+2*n) for n>1. a(n) = 2*a(n2)a(n4) for n>5. G.f.: 2*x^2*(x^3+6*x^2+3*x+2) / ((x1)^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*n6,0),8*n12) \\ _Charles R Greathouse IV_, Jun 28 2013
%K nonn,easy
%O 1,2
%A _Benoit Cloitre_, Oct 02 2006
