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A123170
Continued fraction for (sqrt(2) + 1/sqrt(2))*tanh(1/sqrt(2)).
1
1, 3, 2, 3, 21, 6, 33, 8, 1, 2, 4, 1, 2, 11, 57, 14, 69, 16, 1, 2, 8, 1, 2, 19, 93, 22, 105, 24, 1, 2, 12, 1, 2, 27, 129, 30, 141, 32, 1, 2, 16, 1, 2, 35, 165, 38, 177, 40, 1, 2, 20, 1, 2, 43, 201, 46, 213, 48, 1, 2, 24, 1, 2, 51, 237, 54, 249, 56, 1, 2, 28, 1, 2, 59, 273, 62, 285, 64
OFFSET
1,2
REFERENCES
J. Borwein and D. Bailey, Mathematics by Experiment, Plausible Reasoning in the 21st Century, A. K. Peters, p. 77.
LINKS
FORMULA
For n > 1, a(10*n-9) = 4*n-4, a(10*n-8) = 1, a(10*n-7) = 2, a(10*n-4) = 8*n-5, a(10*n-5) = 36*n-15, a(10*n-4) = 8*n-2, a(10*n-3) = 36*n-3, a(10*n-2) = 8*n, a(10*n-1) = 1, a(10*n) = 2.
Empirical g.f.: x*(2*x^21 +x^20 -2*x^19 -x^18 +3*x^16 +2*x^15 +15*x^14 +5*x^13 -2*x^12 -5*x^11 +2*x^10 +2*x^9 +x^8 +8*x^7 +33*x^6 +6*x^5 +21*x^4 +3*x^3 +2*x^2 +3*x +1) / (x^20 -2*x^10 +1). - Colin Barker, Jun 28 2013
MATHEMATICA
ContinuedFraction[3Tanh[1/Sqrt[2]]/Sqrt[2], 78] (* Benoit Cloitre, Oct 02 2006 *)
PROG
(Magma) SetDefaultRealField(RealField(220)); ContinuedFraction( (Sqrt(2)+1/Sqrt(2))*Tanh(1/Sqrt(2)) ); // G. C. Greubel, Jul 19 2023
(SageMath) continued_fraction_list((sqrt(2)+1/sqrt(2))*tanh(1/sqrt(2)), nterms=100) # G. C. Greubel, Jul 19 2023
CROSSREFS
Sequence in context: A092950 A059239 A350517 * A253381 A091806 A248244
KEYWORD
nonn,cofr
AUTHOR
Benoit Cloitre, Oct 02 2006
STATUS
approved