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A072882
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A nonlinear recurrence of order 3: a(1)=a(2)=a(3)=1; a(n)=(a(n-1)+a(n-2))^2/a(n-3).
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4
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1, 1, 1, 4, 25, 841, 187489, 1418727556, 2393959458891025, 30567386265691995561839449, 658593751358960570203157512237008273218521, 181183406309644143341701434158730639946454023369335051404405528107396
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OFFSET
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1,4
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COMMENTS
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All terms are perfect squares.
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LINKS
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FORMULA
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a(n) ~ 1/9 * c^(((1+sqrt(5))/2)^n), where c = 1.6403763522562240514693138664331346215549... . - Vaclav Kotesovec, May 06 2015
a(n) = 9*a(n-1)*a(n-2) - 2*a(n-1) - 2*a(n-2) - a(n-3).
a(n)*a(n-1)*a(n-2) = ((a(n) + a(n-1) + a(n-2))/3)^2. (End)
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MATHEMATICA
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RecurrenceTable[{a[1]==1, a[2]==1, a[3]==1, a[n]==(a[n-1]+a[n-2])^2/a[n-3]}, a, {n, 1, 10}] (* Vaclav Kotesovec, May 06 2015 *)
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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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STATUS
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approved
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