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A084102
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Inverse binomial transform of A084101.
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9
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1, 2, -2, 0, 4, -8, 8, 0, -16, 32, -32, 0, 64, -128, 128, 0, -256, 512, -512, 0, 1024, -2048, 2048, 0, -4096, 8192, -8192, 0, 16384, -32768, 32768, 0, -65536, 131072, -131072, 0, 262144, -524288, 524288, 0, -1048576, 2097152, -2097152, 0, 4194304, -8388608, 8388608, 0, -16777216, 33554432
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OFFSET
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0,2
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COMMENTS
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The sequence {2, -2, 0, 4, -8, 8, 0, -16, 32, -32, 0, 64, -128, 128, 0, ...} (without the leading 1) is the Lucas V(-2, 2) sequence. - R. J. Mathar, Jan 08 2013
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LINKS
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FORMULA
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a(n) = 2*A009116(n-1), n >= 1, with a(0) = 1.
a(n) = Real part of ( 2*(-1-i)^(n-1) + 2*[n=0] ).
a(n) = 2*(-1)^n*(2*(1+i)^(n-5) + i*(1-i)^(n-3)), n >= 1, with a(0) = 1.
E.g.f.: 2 - exp(-x)*(cos(x) - sin(x)). (End)
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MATHEMATICA
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LinearRecurrence[{-2, -2}, {1, 2, -2}, 50] (* Harvey P. Dale, Aug 09 2017 *)
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PROG
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(Magma) [1] cat [n le 2 select 2*(-1)^(n-1) else -2*(Self(n-1) +Self(n-2)): n in [1..40]]; // G. C. Greubel, Oct 13 2022
(SageMath)
b=BinaryRecurrenceSequence(-2, -2, 2, -2)
def A084102(n): return 1 if (n==0) else b(n-1)
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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