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A086088
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Limit of ratio of consecutive terms in the tetranacci sequence A000078.
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5
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1, 9, 2, 7, 5, 6, 1, 9, 7, 5, 4, 8, 2, 9, 2, 5, 3, 0, 4, 2, 6, 1, 9, 0, 5, 8, 6, 1, 7, 3, 6, 6, 2, 2, 1, 6, 8, 6, 9, 8, 5, 5, 4, 2, 5, 5, 1, 6, 3, 3, 8, 4, 7, 2, 7, 1, 4, 6, 6, 4, 7, 0, 3, 8, 0, 0, 9, 6, 6, 6, 0, 6, 2, 2, 9, 7, 8, 1, 5, 5, 5, 9, 1, 4, 9, 8, 1, 8, 2, 5, 3, 4, 6, 1, 8, 9, 0, 6, 5, 3, 2, 5
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OFFSET
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1,2
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COMMENTS
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The tetranacci constant corresponds to the Golden Section in a fourpartite division 1 = u_1 + u_2 + u_3 + u_4 of a unit line segment, i.e. if 1/u_1 = u_1/u_2 = u_2/u_3 = u_3/u_4 = c, c is the tetranacci constant. - Seppo Mustonen, Apr 19 2005
The other 3 polynomial roots of 1+x+x^2+x^3-x^4 are -0.77480411321543385... and the complex-conjugated pair -0.07637893113374572508475 +- i * 0.814703647170386526841... [From R. J. Mathar, Oct 25 2008]
The continued fraction expansion starts 1, 1, 12, 1, 4, 7, 1, 21, 1, 2, 1, 4, 6, 1, 10, 1, 2, 2, 1, 7, 1, 1,... - R. J. Mathar, Mar 09 2012
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LINKS
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Table of n, a(n) for n=1..102.
Eric Weisstein's World of Mathematics, Tetranacci Number
Eric Weisstein's World of Mathematics, Disk Covering Problem
Eric Weisstein's World of Mathematics, Tetranacci Constant
Eric Weisstein's World of Mathematics, Fibonacci n-Step Number
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EXAMPLE
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1.927561975...
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MATHEMATICA
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RealDigits[Root[ -1-#1-#1^2-#1^3+#1^4&, 2], 10, 110][[1]]
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PROG
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(PARI) real(polroots(1+x+x^2+x^3-x^4)[2]) \\ Charles R Greathouse IV, Jul 19 2012
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CROSSREFS
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Cf. A000078.
Sequence in context: A010537 A172423 A104696 * A203126 A111506 A019733
Adjacent sequences: A086085 A086086 A086087 * A086089 A086090 A086091
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KEYWORD
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nonn,cons
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AUTHOR
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Eric W. Weisstein, Jul 08, 2003
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STATUS
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approved
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