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A276097
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A nonlinear recurrence of order 5: a(1)=a(2)=a(3)=a(4)=a(5)=1; a(n)=(a(n-1)+a(n-2)+a(n-3)+a(n-4))^2/a(n-5).
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3
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1, 1, 1, 1, 1, 16, 361, 143641, 20741472361, 430214650013601071641, 11567790319010747187536221088708755344001, 370675271093071368960746074163948008803845834307486807769098691609909105887376
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OFFSET
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1,6
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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) = 25*a(n-1)*a(n-2)*a(n-3)*a(n-4) - 2a(n-1) - 2a(n-2) - 2a(n-3) - 2a(n-4) - a(n-5).
a(n)*a(n-1)*a(n-2)*a(n-3)*a(n-4) = ((a(n) + a(n-1) + a(n-2) + a(n-3) + a(n-4))/5)^2.
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MATHEMATICA
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RecurrenceTable[{a[1] == a[2] == a[3] == a[4] == a[5] == 1, a[n] == (a[n-1] + a[n-2] + a[n-3] + a[n-4])^2 / a[n-5]}, a, {n, 15}] (* Vincenzo Librandi, Aug 21 2016 *)
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PROG
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(Ruby)
def A(m, n)
a = Array.new(m, 1)
ary = [1]
while ary.size < n
i = a[1..-1].inject(:+)
j = i * i
break if j % a[0] > 0
a = *a[1..-1], j / a[0]
ary << a[0]
end
ary
end
A(5, n)
end
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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