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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

Table of n, a(n) for n=1..58.

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 November 14 04:56 EST 2019. Contains 329110 sequences. (Running on oeis4.)