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Search: id:A139333
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| A139333 |
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Floor of entry (2,1) of [0,1; 1,phi]^n. |
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+0
1
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| 1, 1, 3, 7, 15, 32, 68, 144, 302, 633, 1328, 2783, 5832, 12219, 25604, 53648, 112408, 235529, 493503, 1034034, 2166605, 4539675, 9511953, 19930339, 41759920, 87499309, 183336777
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OFFSET
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1,3
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COMMENT
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a(n)/a(n-1) tends to 2.095293... = exp ArcSinh(phi/2).
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FORMULA
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Floor of entry (2,1) and (1,2) of [0,1; 1,phi]^n. Floor numerators of barover[phi] = [phi, phi, phi,...] where phi = 1.618033989...
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EXAMPLE
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a(5) = 15 since [0,1, 1,phi]^5 = [7.472...,15.708...; 15.708...,32.888...].
a(5) = 15 = floor 15.708203..., since the first five numerators of continued fraction[phi, phi, phi, phi, phi,...] = [1, phi, (phi^2 + 1), (phi^3 + 2*phi), (phi^4 + 3*phi^2 + 1), where (phi^4 + 3*phi^2 + 1) = 15.708203...
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CROSSREFS
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Sequence in context: A132978 A117079 A026745 this_sequence A099444 A132402 A137166
Adjacent sequences: A139330 A139331 A139332 this_sequence A139334 A139335 A139336
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson and Roger L. Bagula (qntmpkt(AT)yahoo.com), Apr 13 2008
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