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A276532 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.

%I A276532 #36 Jan 12 2025 04:52:09
%S A276532 1,1,1,1,1,1,1,2,3,5,11,41,371,7507,429563,419408854,9811194604889,
%T A276532 45615501062085527113,323645006689468299915979814409,
%U A276532 217332607887523478570092794860281557159140687,8092345737591989154121803868154457767563221634145658745306515944569
%N A276532 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.
%C A276532 This sequence is one generalization of Dana Scott's sequence (A048736).
%C A276532 a(n) is an integer for all n.
%C A276532 The recursion exhibits the Laurent phenomenon. See A278706 for the exponents of the denominator of the Laurent polynomial. - _Michael Somos_, Nov 26 2016
%H A276532 Seiichi Manyama, <a href="/A276532/b276532.txt">Table of n, a(n) for n = 0..26</a>
%F A276532 a(n) * a(n-7) = a(n-1) * a(n-6) + a(n-2) * a(n-3) * a(n-4) * a(n-5).
%F A276532 a(6-n) = a(n) for all n in Z.
%o A276532 (Ruby)
%o A276532 def A(k, n)
%o A276532   a = Array.new(k, 1)
%o A276532   ary = [1]
%o A276532   while ary.size < n + 1
%o A276532     i = a[-1] * a[1] + a[2..-2].inject(:*)
%o A276532     break if i % a[0] > 0
%o A276532     a = *a[1..-1], i / a[0]
%o A276532     ary << a[0]
%o A276532   end
%o A276532   ary
%o A276532 end
%o A276532 def A276532(n)
%o A276532   A(7, n)
%o A276532 end
%Y A276532 Cf. A048736, A006721, A276531, A278706.
%K A276532 nonn
%O A276532 0,8
%A A276532 _Seiichi Manyama_, Nov 16 2016