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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, 50384188378657848181032338163962292285660644698840136656562636145266593550842871302412156442811 (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..13.

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

MATHEMATICA

RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==1, a[n]==4a[n-1]a[n-2]a[n-3]-a[n-4]}, a, {n, 15}] (* Harvey P. Dale, Nov 29 2014 *)

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)

a(13) from Harvey P. Dale, Nov 29 2014

STATUS

approved

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Last modified December 21 14:48 EST 2014. Contains 252322 sequences.