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A067361
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17^n cos(2n arctan(1/4)) or denominator of tan(2n arctan(1/4)).
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4
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15, 161, 495, -31679, -1093425, -23647519, -393425745, -4968639359, -35359140465, 375162560801, 21473668418415, 535788072480961, 9867752001506895, 141189807098209121, 1383913884510780975, 713562283940993281, -378544244105385903345
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OFFSET
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1,1
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REFERENCES
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J. M. Borwein and R. Girgensohn, Addition theorems and binary expansions, Canadian J. Math. 47 (1995) 262-273.
E. Eckert, The group of primitive Pythagorean triangles, Mathematics Magazine 57 (1984) 22-27.
S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 430-433.
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LINKS
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Table of n, a(n) for n=1..17.
S. R. Finch, Plouffe's Constant
_Simon Plouffe_, The Computation of Certain Numbers Using a Ruler and Compass, J. Integer Seqs. Vol. 1 (1998), #98.1.3.
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FORMULA
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A(n)=17^n cos(2n arctan(1/4)). A recursive formula for T(n) = tan(2n arctan(1/4)) is T(n+1)=(8/15+T(n))/(1-8/15*T(n)). Unsigned A(n) is the absolute value of denominator of T(n)
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MAPLE
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a[1] := 8/15; for n from 1 to 40 do a[n+1] := (8/15+a[n])/(1-8/15*a[n]):od: seq(abs(numer(a[n])), n=1..40); # a[n]=tan(2n arctan(1/4))
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CROSSREFS
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Cf. A067360 17^n sin(2n arctan(1/4)), Cf. A066770, A066771, A067358, A067359, A020888, A014498, A020892.
Note that A067360, A067361 and 17^n are primitive Pythagorean triples with hypotenuse 17^n.
Sequence in context: A027544 A021048 A095685 * A014920 A081034 A016243
Adjacent sequences: A067358 A067359 A067360 * A067362 A067363 A067364
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KEYWORD
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sign,easy,frac
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AUTHOR
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Barbara Haas Margolius, (b.margolius(AT)csuohio.edu), Jan 17 2002
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STATUS
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approved
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