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A276402 A sequence related to the Somos-6 sequence A006722.

%I A276402 #31 Aug 30 2023 21:14:16
%S A276402 1,1,-1,1,-3,-3,1,-25,49,1,385,1489,503,10753,-82371,-196419,-1575551,
%T A276402 -12482641,95770849,-739310591,5684060161,45018762529,359479836623,
%U A276402 7751171129473,-59488778593731,-137028961472835,-29749898850946559,-441962130410844841
%N A276402 A sequence related to the Somos-6 sequence A006722.
%C A276402 This is the right-hand portion of a two-way infinite sequence ..., 1, -1, 1, 1, 1, 1, -1, 1, -3, -3, 1, -25, 49, 1, 385, 1489, 503, 10753, -82371, ...
%C A276402 0 = a(n+5)*a(n-4) + 2*a(n+4)*a(n-3) - 2*a(n+3)*a(n-2) - 4*a(n+2)*a(n-1) - 5*a(n+1)*a(n) = 2*a(n+5)*a(n-5) + 4*a(n+4)*a(n-4) + 5*a(n+3)*a(n-3) + 19*a(n+2)*a(n-2) + 18*a(n+1)*a(n-1) for all n in Z. - _Michael Somos_, Aug 14 2023
%H A276402 Seiichi Manyama, <a href="/A276402/b276402.txt">Table of n, a(n) for n = 0..206</a>
%H A276402 Yuri N. Fedorov and Andrew N. W. Hone, <a href="http://arxiv.org/abs/1512.00056">Sigma-function solution to the general Somos-6 recurrence via hyperelliptic Prym varieties</a>, arXiv:1512.00056 [nlin.SI], 2015-2016. See Eq. (6.8).
%F A276402 a(0) = a(1) = 1, a(2) = -1, a(3) = 1, a(4) = a(5)= -3, a(n+6)*a(n) = a(n+5)*a(n+1) + 2*a(n+4)*a(n+2) - 2*a(n+3)^2. - _Seiichi Manyama_, Sep 12 2016
%F A276402 a(n) = a(-1-n) for all n in Z. - _Michael Somos_, Aug 14 2023
%t A276402 a[0] = a[1] = 1; a[2] = -1; a[3] = 1; a[4] = a[5] = -3;
%t A276402 a[n_] := a[n] = (-2a[n-3]^2 + 2a[n-4] a[n-2] + a[n-5] a[n-1])/a[n-6];
%t A276402 Table[a[n], {n, 0, 27}] (* _Jean-François Alcover_, Aug 13 2018, after _Seiichi Manyama_ *)
%o A276402 (PARI) {a(n) = if( n>-1 && n<3, [1, 1, -1][n+1], if( n<0, a(-1-n), (a(n-1)*a(n-5) + 2*a(n-2)*a(n-4) - 2*a(n-3)*a(n-3)) / a(n-6)))}; /* _Michael Somos_, Aug 14 2023 */
%Y A276402 Cf. A006722.
%K A276402 sign
%O A276402 0,5
%A A276402 _N. J. A. Sloane_, Sep 12 2016
%E A276402 More terms from _Seiichi Manyama_, Sep 12 2016