[seqfan] g.f. in A157143

[Richard J. Mathar]

Is the generating function in A157143 correct?
The Maple lines
 cx := (1-sqrt(1-4*x))/(2*x) ;
 gx := subs(x=(x/(1+x^2+x^3))^2,cx)*(1-x)/(1+x^2+x^3) ;
 series(%,x=0,50) ;
 gfun[seriestolist](%) ;

based on the A000108 g.f.  generate
1, -1, 0, -1, 1, -1, 2, -2, 4, -5, 8, -13, 18, -32, 46, -77, 123, -192, 325,..

and the 
 mx := (1-x-sqrt(1-2*x-3*x^2))/(2*x^2) ;
 gx := subs(x=(x/(1+x^2+x^3))^2,mx)*(1-x)/(1+x^2+x^3) ;
 series(%,x=0,50) ;
 gfun[seriestolist](%) ;

based on the A000106 (assuming a typo in the formula) g.f. gives
1, -1, 0, -1, 1, -1, 1, -1, 6, 0, -3, -20, 10, 20, 20, -84, -3, 135, 228
and both don't match.