OFFSET
0,6
COMMENTS
This is a (-1,2) generalized Somos-4 sequence.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..166
FORMULA
a(n) = a(3-n) for all n in Z.
0 = a(n)*a(n+4) - a(n+1)*a(n+3) + 2*a(n+2)*a(n+2) for all n in Z.
0 = a(n)*a(n+5) - 2*a(n+1)*a(n+4) + a(n+2)*a(n+3) for all n in Z.
0 = a(n)*a(n+6) - 4*a(n+1)*a(n+5) - 7*a(n+3)*a(n+3) for all n in Z.
0 = a(n)*a(n+7) - a(n+1)*a(n+6) - 8*a(n+3)*a(n+4) for all n in Z.
A242107(2*n-3) = a(n) for all n in Z.
MATHEMATICA
a[0] = a[1] = a[2] = a[3] = 1; a[n_] := a[n] = (a[n - 1]*a[n - 3] - 2*a[n - 2]^2)/a[n - 4]; Array[a, 26, 0] (* Amiram Eldar, Jul 06 2020 *)
PROG
(PARI) {a(n) = my(v); if( n<0, n=3-n); n++; v = vector(max(4, n), k, 1); for(k=5, n, v[k] = (v[k-1] * v[k-3] - 2*v[k-2]^2) / v[k-4]); v[n]};
(PARI) {a(n) = my(m=2*n-3, E=ellinit([1, -1, 0, -1, 1]), z=ellpointtoz(E, [0, 1])); (-1)^n * round(ellsigma(E, m*z) / (ellsigma(E, z)^m^2 * 2^(n^2-3*n+2)))}; /* Michael Somos, Feb 25 2020 */
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Feb 23 2020
STATUS
approved