

A072878


a(n)=4*a(n1)*a(n2)*a(n3)  a(n4).


5



1, 1, 1, 1, 3, 11, 131, 17291, 99665321, 903016046275353, 6224717403288400029624460201, 2240882930472585840954332388399544581477407095086361
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OFFSET

1,5


COMMENTS

A subsequence of the generalized Markoff numbers.


REFERENCES

A. Baragar, Integral solutions of the MarkoffHurwitz equations, J. Number Theory 49 (1994) 2744.


LINKS

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


FORMULA

a(1)=a(2)=a(3)=a(4)=1; a(n)=(a(n1)^2+a(n3)^2+a(n2)^2)/a(n4).
From the recurrence a(n)=4*a(n1)*a(n2)*a(n3)  a(n4), any four successive terms satisfy the MarkoffHurwitz equation a(n)^2+a(n1)^2+a(n2)^2+a(n3)^2=4*a(n)*a(n1)*a(n2)*a(n3), 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^3x^2x1=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



