OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..174
FORMULA
a(n) = A210098(2*n + 1).
0 = a(n)*a(n+4) - a(n+1)*a(n+3) + a(n+2)^2 for all n in Z.
0 = a(n)*a(n+5) - a(n+1)*a(n+4) - 3*a(n+2)*a(n+3) for all n in Z.
0 = a(n+1)^2*a(n+2)^2 - a(n)^2*a(n+3)^2 - a(n)*a(n+2)^3 - a(n+1)^3*a(n+3) - 2*a(n)*a(n+1)*a(n+2)*a(n+3) for all n in Z.
a(n) = -a(-1-n) for all n in Z. - Michael Somos, Mar 14 2020
EXAMPLE
G.f. = 1 + x + 2*x^2 - x^3 - 5*x^4 - 11*x^5 - 7*x^6 + 86*x^7 + 199*x^8 + ...
MATHEMATICA
a[ n_] := a[n] = Which[ n < 0, -a[-1 - n], n < 3, 1 + Boole[n > 1], True, (a[n - 1] a[n - 3] - a[n - 2]^2) / a[n - 4]];
RecurrenceTable[{a[0]==a[1]==1, a[2]==2, a[3]==-1, a[n]==(a[n-1]a[n-3]-a[n-2]^2)/ a[n-4]}, a, {n, 30}] (* Harvey P. Dale, Nov 28 2019 *)
PROG
(PARI) {a(n) = my(v, m); if( n<0, -a(-1 -n), n<3, 1 + (n>1), v = vector( m=n+2, i, (-1)^(i<3) + (i==5)); for( i=6, m, v[i] = (v[i-1] * v[i-3] - v[i-2]^2) / v[i-4]); v[m])};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Oct 08 2016
STATUS
approved