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Search: id:A147316
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| A147316 |
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A000045 Fibonacci mirror sequence Binet: f(n)=(1/5)*2^(-n) ((5 - 2 *Sqrt[5]) (1 + Sqrt[5])^n + (1 - Sqrt[5])^n(5 + 2 * Sqrt[5])). |
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+0
1
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| 1597, -987, 610, -377, 233, -144, 89, -55, 34, -21, 13, -8, 5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597
(list; graph; listen)
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OFFSET
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-14,1
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COMMENT
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The reverse "mirror" sequence has the form of an alternating (-1)^n type.
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FORMULA
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f(n)=(1/5)*2^(-n) ((5 - 2 *Sqrt[5]) (1 + Sqrt[5])^n + (1 - Sqrt[5])^n(5 + 2 * Sqrt[5])).
a(n)=a(n-1)+a(n-2). a(n)=A000045(n-3), n>2. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 30 2008]
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MATHEMATICA
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Clear[f]; f[n_Integer] = Module[{a}, a[n] /. RSolve[{a[n] == a[n - 1] + a[n - 2], a[ -1] == -3, a[0] == 2}, a[n], n][[1]] // FullSimplify]; Table[FullSimplify[ExpandAll[f[n]]], {n, -14, 20}]
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CROSSREFS
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A000285, A022113, A001060, A000045
Sequence in context: A132654 A068131 A068263 this_sequence A078954 A117745 A084427
Adjacent sequences: A147313 A147314 A147315 this_sequence A147317 A147318 A147319
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KEYWORD
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sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 05 2008
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