OFFSET
1,4
EXAMPLE
Iterated decompositions of F=x/(1-x) into [x + a(n)*x^n]:
x = ... o x+6*x^5 o x+2*x^4 o x+1*x^3 o x-1*x^2 o 1*x o F.
These decompositions get closer to x at each iteration:
(1) 1*x o F = x/(1-x) = x + x^2 + x^3 + x^4 + x^5 +...
(2) x-1*x^2 o 1*x o F =
x - x^3 - 2*x^4 - 3*x^5 - 4*x^6 - 5*x^7 - 6*x^8 -...
(3) x+1*x^3 o x-1*x^2 o 1*x o F =
x - 2*x^4 - 6*x^5 - 10*x^6 - 11*x^7 - 6*x^8 + 7*x^9 +...
(4) x+2*x^4 o x+1*x^3 o x-1*x^2 o 1*x o F =
x - 6*x^5 - 10*x^6 - 27*x^7 - 54*x^8 - 73*x^9 +...
(5) x+6*x^5 o x+2*x^4 o x+1*x^3 o x-1*x^2 o 1*x o F =
x - 10*x^6 - 27*x^7 - 54*x^8 - 253*x^9 +...
PROG
(PARI) {a(n)=local(F=x/(1-x+x*O(x^n))); if(n<1, 0, if(n==1, 1, for(k=2, n, c=-polcoeff(F, k); F=subst(x+c*x^k, x, F); ); return(c)))}
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, May 20 2006
STATUS
approved