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Search: id:A139030
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| A139030 |
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Real part of (4 + 3i)^n. |
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+0
2
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| 4, 7, -44, -527, -3116, -11753, -16124, 164833, 1721764, 9653287, 34182196, 32125393, -597551756, -5583548873, -29729597084, -98248054847, -42744511676
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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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FORMULA
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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 (ppl(AT)spl.at), Jul 08 2008
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EXAMPLE
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a(5) = -3116 since (4 + 3i)^5 = (-3116 - 237i) where -237 = A139031(5).
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CROSSREFS
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Cf. A139031, A066771, A066776.
Sequence in context: A152450 A059213 A093102 this_sequence A115439 A094609 A049191
Adjacent sequences: A139027 A139028 A139029 this_sequence A139031 A139032 A139033
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KEYWORD
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sign
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 06 2008
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