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URL: https://oeis.org/A330383

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A330383
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.
1
1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 13, 19, 49, 139, 349, 814, 1999, 6239, 17319, 88463, 352207, 1433335, 4638463, 24497167, 115269646, 734764861, 5312141131, 33794633761, 194109246131, 1155202458861, 11655116287031, 94020049884421, 1124623970095267
OFFSET
0,9
COMMENTS
The sequence is similar to Somos-8 but all of the terms are integers.
LINKS
FORMULA
a(n) = a(7-n) for all n in Z.
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.
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.
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.
MATHEMATICA
nxt[{a1_, a2_, a3_, a4_, a5_, a6_, a7_, a8_}]:={a2, a3, a4, a5, a6, a7, a8, (a8*a2+a7*a3-a6*a4+a5^2)/a1}; NestList[nxt, PadRight[{}, 8, 1], 30][[;; , 1]] (* Harvey P. Dale, Nov 10 2025 *)
PROG
(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])};
CROSSREFS
Sequence in context: A188754 A108310 A252398 * A146999 A147485 A341650
KEYWORD
nonn
AUTHOR
Michael Somos, Mar 03 2020
STATUS
approved