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A112572
G.f. A(x) satisfies: A(x)^4 equals the g.f. of A110638, which consists entirely of numbers 1 through 8.
0
1, 1, -1, 3, -6, 18, -52, 156, -481, 1512, -4828, 15621, -51081, 168537, -560309, 1874975, -6309964, 21341241, -72497698, 247247463, -846187023, 2905210526, -10003144986, 34532780087, -119499263663, 414431066955, -1440182574644, 5014115406096
OFFSET
0,4
COMMENTS
A110638 is formed from every 2nd term of A083948, which also consists entirely of numbers 1 through 8.
FORMULA
G.f. A(x) satisfies: A(x)^8 (mod 16) = g.f. of A083948.
EXAMPLE
A(x) = 1 + x - x^2 + 3*x^3 - 6*x^4 + 18*x^5 - 52*x^6 + 156*x^7 +...
A(x)^4 = 1 + 4*x + 2*x^2 + 4*x^3 + 7*x^4 + 8*x^5 + 4*x^6 +...
A(x)^8 = 1 + 8*x + 20*x^2 + 24*x^3 + 50*x^4 + 88*x^5 + 116*x^6 +...
A(x)^8 (mod 16) = 1 + 8*x + 4*x^2 + 8*x^3 + 2*x^4 + 8*x^5 +...
G(x) = 1 + 8*x + 4*x^2 + 8*x^3 + 2*x^4 + 8*x^5 + 4*x^6 + 8*x^7 +...
where G(x) is the g.f. of A083948.
PROG
(PARI) {a(n)=local(d=2, m=8, A=1+m*x); for(j=2, d*n, for(k=1, m, t=polcoeff((A+k*x^j+x*O(x^j))^(1/m), j); if(denominator(t)==1, A=A+k*x^j; break))); polcoeff(Ser(vector(n+1, i, polcoeff(A, d*(i-1))))^(1/4), n)}
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Sep 14 2005
STATUS
approved