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A072878 a(n)=4*a(n-1)*a(n-2)*a(n-3) - a(n-4). 5
1, 1, 1, 1, 3, 11, 131, 17291, 99665321, 903016046275353, 6224717403288400029624460201, 2240882930472585840954332388399544581477407095086361 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

A subsequence of the generalized Markoff numbers.

REFERENCES

A. Baragar, Integral solutions of the Markoff-Hurwitz equations, J. Number Theory 49 (1994) 27-44.

LINKS

Table of n, a(n) for n=1..12.

FORMULA

a(1)=a(2)=a(3)=a(4)=1; a(n)=(a(n-1)^2+a(n-3)^2+a(n-2)^2)/a(n-4).

From the recurrence a(n)=4*a(n-1)*a(n-2)*a(n-3) - a(n-4), any four successive terms satisfy the Markoff-Hurwitz equation a(n)^2+a(n-1)^2+a(n-2)^2+a(n-3)^2=4*a(n)*a(n-1)*a(n-2)*a(n-3), cf. A075276. As n tends to infinity, the limit of log(log(a(n)))/n is log x = 0.6093778633... where x=1.839286755... is the real root of the cubic x^3-x^2-x-1=0. - Andrew Hone (anwh(AT)kent.ac.uk), Nov 14 2005

CROSSREFS

Cf. A075276, A072879.

Sequence in context: A201611 A088075 A088076 * A112957 A057205 A121897

Adjacent sequences:  A072875 A072876 A072877 * A072879 A072880 A072881

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Jul 28 2002

EXTENSIONS

Entry revised Nov 19, 2005, based on comments from Andrew Hone (anwh(AT)kent.ac.uk)

STATUS

approved

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Last modified October 20 14:03 EDT 2014. Contains 248331 sequences.