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A072878
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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.
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14
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1, 1, 1, 1, 3, 11, 131, 17291, 99665321, 903016046275353, 6224717403288400029624460201, 2240882930472585840954332388399544581477407095086361, 50384188378657848181032338163962292285660644698840136656562636145266593550842871302412156442811
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OFFSET
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1,5
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COMMENTS
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A subsequence of the generalized Markoff numbers.
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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Entry revised Nov 19 2005, based on comments from Andrew Hone
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STATUS
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approved
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