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 A123169 Continued fraction for sqrt(1/2)*(exp(sqrt(1/2))-1)/(exp(sqrt(1/2))+1). 1
 0, 4, 6, 20, 14, 36, 22, 52, 30, 68, 38, 84, 46, 100, 54, 116, 62, 132, 70, 148, 78, 164, 86, 180, 94, 196, 102, 212, 110, 228, 118, 244, 126, 260, 134, 276, 142, 292, 150, 308, 158, 324, 166, 340, 174, 356, 182, 372, 190, 388, 198, 404, 206, 420, 214, 436, 222, 452 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This continued fraction shows exp(sqrt(1/2)) is irrational. REFERENCES J. Borwein and D. Bailey, Mathematics by experiment, plausible reasoning in the 21st Century, A. K. Peters, p. 77 LINKS Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1). FORMULA a(1)=0, for n>=1 a(2n)=16n-12, a(2n+1)=8n-2. 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 MAPLE A123169:=n->(3+(-1)^n)*(-3+2*n): 0, seq(A123169(n), n=2..100); # Wesley Ivan Hurt, Apr 27 2017 PROG (PARI) a(n)=if(n%2, max(4*n-6, 0), 8*n-12) \\ Charles R Greathouse IV, Jun 28 2013 CROSSREFS Sequence in context: A012969 A057789 A174936 * A205955 A023863 A024480 Adjacent sequences:  A123166 A123167 A123168 * A123170 A123171 A123172 KEYWORD nonn,easy AUTHOR Benoit Cloitre, Oct 02 2006 STATUS approved

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Last modified May 25 17:19 EDT 2020. Contains 334595 sequences. (Running on oeis4.)