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A276534
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a(n) = a(n-1) * a(n-4) * (a(n-2) * a(n-3) + 1) / a(n-5), with a(0) = a(1) = a(2) = a(3) = a(4) = 1.
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2
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1, 1, 1, 1, 1, 2, 4, 12, 108, 10584, 27454896, 94148851006224, 246222177535609206635748240, 62371770277951054762478578990896212287188931341600, 3750595553941161278345366267513070968239986992860645038477600300348697171928615364721752014400
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,6
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COMMENTS
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Inspired by Somos-5 sequence.
a(n) is integer for n >= 0.
a(n+1)/a(n) is integer for n >= 0.
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LINKS
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FORMULA
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a(n) * a(n-5) = a(n-1) * a(n-4) + a(n-1) * a(n-2) * a(n-3) * a(n-4).
a(4-n) = a(n).
Let b(n) = b(n-4) * (b(n-2) * (b(0) * b(1) * ... * b(n-3))^2 + 1) with b(0) = b(1) = b(2) = b(3) = 1, then a(n) = a(n-1) * b(n-1) = b(0) * b(1) * ... * b(n-1) for n > 0.
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EXAMPLE
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a(5) = a(4) * b(4) = 1 * 2 = 2,
a(6) = a(5) * b(5) = 2 * 2 = 4,
a(7) = a(6) * b(6) = 4 * 3 = 12,
a(8) = a(7) * b(7) = 12 * 9 = 108.
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PROG
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(Ruby)
def A(k, n)
a = Array.new(2 * k + 1, 1)
ary = [1]
while ary.size < n + 1
i = 0
k.downto(1){|j|
i += 1
i *= a[j] * a[-j]
}
break if i % a[0] > 0
a = *a[1..-1], i / a[0]
ary << a[0]
end
ary
end
A(2, 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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