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A139030
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Real part of (4 + 3i)^n.
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1
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4, 7, -44, -527, -3116, -11753, -16124, 164833, 1721764, 9653287, 34182196, 32125393, -597551756, -5583548873, -29729597084, -98248054847, -42744511676, 2114245277767, 17982575014036, 91004468168113, 278471369994004, -47340744250793, -7340510203856444
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| sqrt (a(n)^2 + (A139031(n))^2) = 5^n. Example: a(3) = -44, A139031(3) = 117. Sqrt (-44^2 + 117^2) = 5^3.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (8,-25).
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FORMULA
| Real part of (4 + 3i)^n. Term (1,1) of [4,-3; 3,4]^n a(n), n>2 = 8*a(n-1) - 25*a(n-2), given a(1) = 4, a(2) = 7. Odd indexed terms of A066776 interleaved with even indexed terms of A066771, irrespective of sign.
a(n)=[2-(3/2)*I]*(4-3*I)^n+[2+(3/2)*I]*(4+3*I)^n, with n>=0 and I=sqrt(-1) - Paolo P. Lava (paoloplava(AT)gmail.com), Jul 08 2008
G.f. -x*(-4+25*x) / ( 1-8*x+25*x^2 ). - R. J. Mathar, Feb 05 2011
a(1)=4, a(2)=7, a(n)=8*a(n-1)-25*a(n-2) [From Harvey P. Dale, Nov 09 2011]
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EXAMPLE
| a(5) = -3116 since (4 + 3i)^5 = (-3116 - 237i) where -237 = A139031(5).
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MATHEMATICA
| Re[(4+3I)^Range[40]] (* or *) LinearRecurrence[{8, -25}, {4, 7}, 40] (* From Harvey P. Dale, Nov 09 2011 *)
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CROSSREFS
| Cf. A139031, A066771, A066776.
Sequence in context: A059213 A093102 A199404 * A115439 A192168 A094609
Adjacent sequences: A139027 A139028 A139029 * A139031 A139032 A139033
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KEYWORD
| sign
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 06 2008
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EXTENSIONS
| More terms from Harvey P. Dale, Nov 09 2011
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