A112571 G.f. A(x) satisfies: A(x)^2 equals the g.f. of A110637, which consists entirely of numbers 1 through 8.

1, 1, 3, -1, -2, 6, 0, -16, 23, 40, -140, 13, 591, -827, -1577, 5887, -500, -27095, 38922, 77859, -295183, 21310, 1428714, -2069421, -4295099, 16345171, -921876, -81760620, 118435457, 253839799, -963510264, 37372170, 4936868645, -7119213992, -15717478733, 59293735690

Offset: 0

Author

Paul D. Hanna, Sep 14 2005

Keywords

• sign

Comments

A110637 is formed from every 4th term of A083948, which also consists entirely of numbers 1 through 8.

Examples

			A(x) = 1 + x + 3*x^2 - x^3 - 2*x^4 + 6*x^5 - 16*x^7 + 23*x^8 +...
A(x)^2 = 1 + 2*x + 7*x^2 + 4*x^3 + 3*x^4 + 2*x^5 + x^6 + 8*x^7 +...
A(x)^8 = 1 + 8*x + 52*x^2 + 216*x^3 + 754*x^4 + 2008*x^5 +...
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.
		

Crossrefs

Cf. A110637, A083948.

Programs

PARI

{a(n)=local(d=4,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))))^(1/2),n)}

Formula

G.f. A(x) satisfies: A(x)^8 (mod 16) = g.f. of A083948.