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A276532
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a(n) = (a(n-1) * a(n-6) + a(n-2) * a(n-3) * a(n-4) * a(n-5)) / a(n-7), with a(0) = a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = 1.
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3
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1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 11, 41, 371, 7507, 429563, 419408854, 9811194604889, 45615501062085527113, 323645006689468299915979814409, 217332607887523478570092794860281557159140687, 8092345737591989154121803868154457767563221634145658745306515944569
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listen;
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OFFSET
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0,8
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COMMENTS
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This sequence is one generalization of Dana Scott's sequence (A048736).
a(n) is integer for all n.
The recursion exhibits the Laurent phenomenon. See A278706 for the exponents of the denominator of the Laurent polynomial. - Michael Somos, Nov 26 2016
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LINKS
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FORMULA
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a(n) * a(n-7) = a(n-1) * a(n-6) + a(n-2) * a(n-3) * a(n-4) * a(n-5).
a(6-n) = a(n) for all n in Z.
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PROG
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(Ruby)
def A(k, n)
a = Array.new(k, 1)
ary = [1]
while ary.size < n + 1
i = a[-1] * a[1] + a[2..-2].inject(:*)
break if i % a[0] > 0
a = *a[1..-1], i / a[0]
ary << a[0]
end
ary
end
A(7, 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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