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 A072878 a(n) = 4*a(n-1)*a(n-2)*a(n-3) - a(n-4) with a(1) = a(2) = a(3) = a(4) = 1. 14
 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. LINKS Seiichi Manyama, Table of n, a(n) for n = 1..16 Arthur Baragar, Integral solutions of the Markoff-Hurwitz equations, J. Number Theory 49 (1994), 27-44. Andrew N. W. Hone, Diophantine non-integrability of a third order recurrence with the Laurent property, arXiv:math/0601324 [math.NT], 2006. Andrew N. W. Hone, Diophantine non-integrability of a third order recurrence with the Laurent property, J. Phys. A: Math. Gen. 39 (2006), L171-L177. Matthew Christopher Russell, Using experimental mathematics to conjecture and prove theorems in the theory of partitions and commutative and non-commutative recurrence, PhD Dissertation, Mathematics Department, Rutgers University, May 2016. 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) for n >= 5. 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, Nov 14 2005 MATHEMATICA RecurrenceTable[{a==a==a==a==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. A022405, A064098, A075276, A072879, A072880. Sequence in context: A088076 A276258 A284604 * 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 a(13) from Harvey P. Dale, Nov 29 2014 Name clarified by Petros Hadjicostas, May 11 2019 STATUS approved

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Last modified July 29 02:55 EDT 2021. Contains 346340 sequences. (Running on oeis4.)