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A067359
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Real part of (5 + 12i)^n.
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3
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1, 5, -119, -2035, -239, 341525, 3455641, -23161315, -815616479, -4241902555, 95420159401, 1671083125805, 584824319281, -276564805068235, -2864483360640839, 18094618450123325, 665043872449535041, 3592448206424508485, -76467932379726337079, -1371803070683005304755
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OFFSET
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1,2
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COMMENTS
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Also 13^n*cos(2*n*arctan(2/3)) or denominator of tan(2*n*arctan(2/3)).
Note that A067358(n), a(n) and 13^n are primitive Pythagorean triples with hypotenuse 13^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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G.f.: (1-5*x)/(1-10*x+169*x^2).
a(n) = 10*a(n-1) - 169*a(n-2). (End)
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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(denom(a[n])), n=1..40); # a[n]=tan(2n arctan(2/3))
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MATHEMATICA
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PROG
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(PARI) a(n)=real((5+12*I)^n)
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CROSSREFS
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Cf. A067358 (13^n sin(2n arctan(2/3))).
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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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STATUS
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approved
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