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A276095
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A nonlinear recurrence of order 4: a(1)=a(2)=a(3)=a(4)=1; a(n)=(a(n-1)+a(n-2)+a(n-3))^2/a(n-4).
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5
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1, 1, 1, 1, 9, 121, 17161, 298978681, 9933176210033041, 815437979830770470704295274609, 38747106750801481775941360512378545527545442200632960401
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OFFSET
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1,5
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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) = 16*a(n-1)*a(n-2)*a(n-3) - 2a(n-1) - 2a(n-2) - 2a(n-3) - a(n-4).
a(n)*a(n-1)*a(n-2)*a(n-3) = ((a(n) + a(n-1) + a(n-2) + a(n-3))/4)^2.
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MATHEMATICA
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RecurrenceTable[{a[n] == (a[n - 1] + a[n - 2] + a[n - 3])^2/a[n - 4], a[1] == a[2] == a[3] == a[4] == 1}, a, {n, 1, 12}] (* Michael De Vlieger, Aug 18 2016 *)
nxt[{a_, b_, c_, d_}]:={b, c, d, (b+c+d)^2/a}; NestList[nxt, {1, 1, 1, 1}, 10][[;; , 1]] (* Harvey P. Dale, Aug 20 2024 *)
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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(4, 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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