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Search: id:A143056
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| A143056 |
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The real part of complex sequence: a(n)=(1+I)*a(n-1)+a(n-1). |
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+0
1
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| 0, 1, 1, 1, 0, -3, -9, -19, -32, -43, -39, 5, 128, 377, 783, 1305, 1728, 1513, -367, -5495, -15744, -32267, -53177, -69371, -58464, 21693, 235305, 656909, 1328896, 2165489, 2781855
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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The ratio real absolute value approaches:1.7000157758867898
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FORMULA
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a(n)=(1+I)*a(n-1)+a(n-1); a(n)_out=realpart(a(n)).
G.f.: x^2*(1-x-x^2)/(1-2x+2x^3+x^4). a(n)= 2*a(n-1) -2*a(n-3) -a(n-4). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 24 2008]
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EXAMPLE
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The imaginary part is:
{0, 0, 1, 2, 4, 6, 7, 4, -8, -36, -87, -162, -244, -278, -145, 360,
1520, 3608, 6641, 9882, 11028, 5166, -16073, -64084, -149528, -272076,
-399911, -436682, -179684, 712530, 2698335}
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MATHEMATICA
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Clear[a, n]; a[0] = 0; a[1] = 1; a[n_] := a[n] = (1+I)*a[n - 1] + a[n - 2]; Table[Re[a[n]], {n, 0, 30}]
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CROSSREFS
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Sequence in context: A029479 A014869 A018495 this_sequence A066506 A058331 A049749
Adjacent sequences: A143053 A143054 A143055 this_sequence A143057 A143058 A143059
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KEYWORD
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uned,sign
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 13 2008
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