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Tetranacci Constant

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The tetranacci constant T is the limit of the ratios T_(n+1)/T_n, where T_n denotes the nth tetranacci number. It is given by

T=(x^4-x^3-x^2-x-1)_2
(1)
=1.92756...
(2)

(OEIS A086088), where (P(x))_n denotes the nth polynomial root.

The tetranacci constant satisfies the identity

T+T^(-4)=2.
(3)

The constant also describes a division of a line segment of length 1 into 4 parts in continuous proportion (Mustonen 2005, pp. 2-3). The lengths are T^(-1), T^(-2), T^(-3), and T^(-4), whose sum is 1. This is the n=4 case of the geometric interpretation of the limiting ratios of Fibonacci n-step numbers.

See also

Fibonacci n-Step Number, Tetranacci Number, Tribonacci Constant

Portions of this entry contributed by Jonathan Vos Post

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References

Mustonen, S. "Extension of Golden Section to Multiple-Partite Division of a Line Segment." Apr. 24, 2005. https://www.survo.fi/papers/nsection.pdf.Sloane, N. J. A. Sequence A086088 in "The On-Line Encyclopedia of Integer Sequences."Waddill, M. E. "The Tetranacci Sequence and Generalizations." Fib. Quart. 30, 9-20, 1992.Waddill, M. E. "Some Properties of the Tetranacci Sequence Modulo m." Fib. Quart. 30, 232-238, 1992.

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Tetranacci Constant

Cite this as:

Weisstein, Eric W., with contributions by Jonathan Vos Post. "Tetranacci Constant." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TetranacciConstant.html

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