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A067360
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a(n) = 17^n sin(2n arctan(1/4)) or numerator of tan(2n arctan(1/4)).
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4
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8, 240, 4888, 77280, 905768, 4839120, -116593352, -4896306240, -113193708472, -1980778750800, -26710380775592, -228866364286560, 853309115549288, 91741652745294480, 2505643247965090168, 48655959795562600320, 735547895204966951048
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OFFSET
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1,1
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COMMENTS
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Note that A067360(n), A067361(n) and 17^n are primitive Pythagorean triples with hypotenuse 17^n.
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 430-433.
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LINKS
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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).
G.f.: 8*x / (1 - 30*x + 289*x^2).
a(n) = i*((15 - 8*i)^n - (15 + 8*i)^n)/2 where i=sqrt(-1).
a(n) = 30*a(n-1) - 289*a(n-2) for n>2.
(End)
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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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MATHEMATICA
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Table[Tan[2n ArcTan[1/4]] // TrigToExp // Simplify // Numerator, {n, 1, 17} ] (* Jean-François Alcover, Jul 25 2017 *)
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CROSSREFS
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Cf. A067361 (17^n cos(2n arctan(1/4))).
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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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