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A121622
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Real part of (3 + 2i)^n.
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4
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1, 3, 5, -9, -119, -597, -2035, -4449, -239, 56403, 341525, 1315911, 3455641, 3627003, -23161315, -186118929, -815616479, -2474152797, -4241902555, 6712571031, 95420159401, 485257533003, 1671083125805, 3718150825791, 584824319281
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OFFSET
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0,2
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COMMENTS
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Companion sequence A121621 is Re(2 + 3i)^n.
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LINKS
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Table of n, a(n) for n=0..24.
Index to sequences with linear recurrences with constant coefficients, signature (6,-13).
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FORMULA
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a(n) = Re(3 + 2i)^n.
a(n) = 6*a(n-1) - 13*a(n-2).
a(n)=(1/2)*(3-2*I)^n+(1/2)*(3+2*I)^n, with n>=0 and I=sqrt(-1) - Paolo P. Lava, Jun 25 2008
G.f. ( 1-3*x ) / ( 1-6*x+13*x^2 ). - R. J. Mathar, Aug 12 2012
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EXAMPLE
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a(5) = -597 since (3 + 2i)^5 = (-597 + 122i).
a(5) = -597 = 6*(-119) - 13*(-9) = 6*a(5) -13*a(4).
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MATHEMATICA
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f[n_] := Re[(3 + 2I)^n]; Table[f[n], {n, 0, 24}] - Robert G. Wilson v, Aug 17 2006
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CROSSREFS
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Cf. A121621.
Cf. A193410, A066771.
Sequence in context: A163550 A123220 A098339 * A188983 A083519 A211414
Adjacent sequences: A121619 A121620 A121621 * A121623 A121624 A121625
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KEYWORD
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sign,easy
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AUTHOR
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Gary W. Adamson and Nick Williams, Aug 10 2006
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EXTENSIONS
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More terms from Robert G. Wilson v, Aug 17 2006
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STATUS
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approved
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