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A256916 a(n) = (a(n-1) * a(n-5) + a(n-3)^2) / a(n-6) with a(0) = a(1) = 1, a(2) = 0, a(3) = -1, a(4) = -3, a(8) = 29.

%I A256916 #15 Sep 08 2022 08:46:12
%S A256916 1,1,0,-1,-3,-3,-2,9,29,83,56,-243,-2351,-7227,-18648,54011,698301,
%T A256916 5324929,15128062,-28437275,-1438167267,-14356619593,-108319050672,
%U A256916 80689859625,13472837856577,268773209122329,2678522836045616,7565687047045511,-672545703786704803
%N A256916 a(n) = (a(n-1) * a(n-5) + a(n-3)^2) / a(n-6) with a(0) = a(1) = 1, a(2) = 0, a(3) = -1, a(4) = -3, a(8) = 29.
%C A256916 Similar to the Somos-6 and Somos-7 sequences with many bilinear identities.
%H A256916 G. C. Greubel, <a href="/A256916/b256916.txt">Table of n, a(n) for n = 0..208</a>
%F A256916 a(n) = a(-n) for all n in Z.
%F A256916 a(n) = A256858(2*n) for all n in Z.
%F A256916 Let b(n) = A102276(n). Then 0 = a(n) * b(n) - a(n+2) * b(n-2) + a(n+3) * b(n-3) for all n in Z.
%F A256916 0 = a(n) * a(n+6) - a(n+1) * a(n+5) - a(n+3) * a(n+3) for all n in Z.
%F A256916 0 = a(n) * a(n+9) + a(n+2) * a(n+7) - a(n+3) * a(n+6) - 9 * a(n+4) * a(n+5) for all n in Z.
%t A256916 Join[{1,1,0,-1,-3,-3,-2,9,29}, RecurrenceTable[{a[n] == (a[n-1]*a[n-5] + a[n-3]^2)/a[n-6], a[9] == 83, a[10] == 56, a[11] == -243, a[12] == -2351, a[13] == -7227, a[14] == -18648}, a, {n, 9, 60}]] (* _G. C. Greubel_, Aug 03 2018 *)
%o A256916 (PARI) {a(n) = my(an); n = abs(n)+1; an = concat([ 1, 1, 0, -1, -3, -3, -2, 9, 29], vector(max(0, n-9), k)); for(k=10, n, an[k] = (an[k-1] * an[k-5] + an[k-3]^2) / an[k-6]); an[n]};
%o A256916 (Magma) I:=[83, 56, -243, -2351, -7227, -18648]; [1,1,0,-1,-3,-3,-2,9,29] cat [n le 6 select I[n] else (Self(n-1)*Self(n-5) + Self(n-3)^2)/ Self(n-6): n in [1..30]]; // _G. C. Greubel_, Aug 03 2018
%Y A256916 Cf. A102276, A256858.
%K A256916 sign
%O A256916 0,5
%A A256916 _Michael Somos_, Apr 13 2015