A330383 - OEIS

%I #26 Mar 04 2020 07:37:15

%S 1,1,1,1,1,1,1,1,2,3,5,7,13,19,49,139,349,814,1999,6239,17319,88463,

%T 352207,1433335,4638463,24497167,115269646,734764861,5312141131,

%U 33794633761,194109246131,1155202458861,11655116287031,94020049884421,1124623970095267

%N a(n) = (a(n-1)*a(n-7) + a(n-2)*a(n-6) - a(n-3)*a(n-5) + a(n-4)^2) / a(n-8), a(0) = ... = a(7) = 1.

%C The sequence is similar to Somos-8 but all of the terms are integers.

%H Seiichi Manyama, <a href="/A330383/b330383.txt">Table of n, a(n) for n = 0..252</a>

%F a(n) = a(7-n) for all n in Z.

%F a(n)*a(n+8) = a(n+1)*a(n+7) + a(n+2)*a(n+6) - a(n+3)*a(n+5) + a(n+4)^2 for all n in Z.

%F a(n)*a(n+9) = -a(n+1)*a(n+8) + 3*a(n+2)*a(n+7) + a(n+3)*a(n+6) + a(n+4)*a(n+5) for all n in Z.

%F 0 = + a(n+6)*a(n+3)*a(n) - a(n+6)*a(n+2)*a(n+1) - a(n+5)*a(n+4)*a(n) - a(n+5)*a(n+3)*a(n+1) + 2*a(n+5)*a(n+2)^2 + 2*a(n+4)^2*a(n+1) - 3*a(n+4)*a(n+3)*a(n+2) + a(n+3)^3 for all n in Z.

%o (PARI) {a(n) = my(v); if( n<0, n=7-n); if( n<8, 1, n++; v=vector(n, k, 1); for( k=9, n, v[k] = (v[k-1]*v[k-7] + v[k-2]*v[k-6] - v[k-3]*v[k-5] + v[k-4]^2) / v[k-8]); v[n])};

%K nonn

%O 0,9

%A _Michael Somos_, Mar 03 2020