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Search: id:A067358
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| A067358 |
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Imaginary part of (5+12i)^n. |
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+0
4
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| 0, 12, 120, -828, -28560, -145668, 3369960, 58317492, 13651680, -9719139348, -99498527400, 647549275812, 23290743888720, 123471611274972, -2701419604443960, -47880898349909868, -22269070348069440, 7869181117654073292, 82455284065364468280, -505338768229893703548
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Also 13^n sin(2n arctan(2/3)) or numerator of tan(2n arctan(2/3)).
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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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G.f.: 12*x/(1-10*x+169*x^2). a(n)=10*a(n-1)-169*a(n-2). - Michael Somos
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MAPLE
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a[1] := 12/5; for n from 1 to 40 do a[n+1] := (12/5+a[n])/(1-12/5*a[n]):od: seq(abs(numer(a[n])), n=1..40); # a[n]=tan(2n arctan(2/3))
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PROGRAM
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(PARI) a(n)=imag((5+12*I)^n)
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CROSSREFS
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Cf. A067359 13^n cos(2n arctan(2/3)), Cf. A066770, A066771, A067360, A067361, A020888, A014498, A020892.
Note that a(n), A067359 and 13^n are primitive Pythagorean triples with hypotenuse 13^n.
Adjacent sequences: A067355 A067356 A067357 this_sequence A067359 A067360 A067361
Sequence in context: A056320 A056311 A009050 this_sequence A061506 A059155 A012443
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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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EXTENSIONS
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Better description from Michael Somos, Jun 27, 2002
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