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Search: id:A067360
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| A067360 |
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17^n sin(2n arctan(1/4)) or numerator of tan(2n arctan(1/4)). |
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+0
4
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| 8, 240, 4888, 77280, 905768, 4839120, -116593352, -4896306240, -113193708472, -1980778750800, -26710380775592, -228866364286560, 853309115549288, 91741652745294480, 2505643247965090168, 48655959795562600320, 735547895204966951048
(list; graph; listen)
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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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S. R. Finch, Plouffe's Constant
S. 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 sin(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 numerator 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. A067361 17^n cos(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: A111836 A134504 A145418 this_sequence A007060 A158263 A115613
Adjacent sequences: A067357 A067358 A067359 this_sequence A067361 A067362 A067363
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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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