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A276535 a(n) = a(n-1) * a(n-6) * (a(n-2) * a(n-5) * (a(n-3) * a(n-4) + 1) + 1) / a(n-7), with a(0) = a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = 1.

%I A276535 #33 Jan 12 2025 05:00:01
%S A276535 1,1,1,1,1,1,1,3,9,63,2331,4114215,16341764835375,
%T A276535 266584861903285121344257375,
%U A276535 7896333852271846954822982651737848156847060737115875,2309336603704915706429640788623787983392652603516450553629239932054220008270731649775618317371336467375
%N A276535 a(n) = a(n-1) * a(n-6) * (a(n-2) * a(n-5) * (a(n-3) * a(n-4) + 1) + 1) / a(n-7), with a(0) = a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = 1.
%C A276535 Inspired by Somos-7 sequence.
%C A276535 a(n) is an integer for n >= 0.
%C A276535 a(n+1)/a(n) is an integer for n >= 0.
%H A276535 Seiichi Manyama, <a href="/A276535/b276535.txt">Table of n, a(n) for n = 0..18</a>
%F A276535 a(n) * a(n-7) = a(n-1) * a(n-6) + a(n-1) * a(n-2) * a(n-5) * a(n-6) + a(n-1) * a(n-2) * a(n-3) * a(n-4) * a(n-5) * a(n-6).
%F A276535 a(6-n) = a(n).
%F A276535 Let b(n) = b(n-6) * (b(n-2) * b(n-3) * b(n-4) * (b(0) * b(1) * ... * b(n-5))^2 * (b(n-3) * (b(0) * b(1) * ... * b(n-4))^2 + 1)+ 1) with b(0) = b(1) = b(2) = b(3) = b(4) = b(5) = 1, then a(n) = a(n-1) * b(n-1) = b(0) * b(1) * ... * b(n-1) for n > 0.
%e A276535 a(7) = a(6) * b(6) = 1 * 3 = 3,
%e A276535 a(8) = a(7) * b(7) = 3 * 3 = 9,
%e A276535 a(9) = a(8) * b(8) = 9 * 7 = 63,
%e A276535 a(10) = a(9) * b(9) = 63 * 37 = 2331.
%o A276535 (Ruby)
%o A276535 def A(k, n)
%o A276535   a = Array.new(2 * k + 1, 1)
%o A276535   ary = [1]
%o A276535   while ary.size < n + 1
%o A276535     i = 0
%o A276535     k.downto(1){|j|
%o A276535       i += 1
%o A276535       i *= a[j] * a[-j]
%o A276535     }
%o A276535     break if i % a[0] > 0
%o A276535     a = *a[1..-1], i / a[0]
%o A276535     ary << a[0]
%o A276535   end
%o A276535   ary
%o A276535 end
%o A276535 def A276535(n)
%o A276535   A(3, n)
%o A276535 end
%Y A276535 Cf. A006723, A276534.
%K A276535 nonn
%O A276535 0,8
%A A276535 _Seiichi Manyama_, Nov 16 2016