A143046 G.f. A(x) satisfies A(x) = 1 + x*A(-x)^3.

1, 1, -3, -6, 35, 87, -588, -1578, 11511, 32223, -245883, -706824, 5556564, 16267508, -130617600, -387533058, 3161190783, 9474886287, -78241316361, -236394953670, 1971270824859, 5994591989967, -50388913722480, -154052058035736

Offset: 0

Author

Paul D. Hanna, Jul 19 2008

Keywords

• sign

Examples

			G.f.: A(x) = 1 + x - 3*x^2 - 6*x^3 + 35*x^4 + 87*x^5 - 588*x^6 - 1578*x^7 +...
where
A(x)^3 = 1 + 3*x - 6*x^2 - 35*x^3 + 87*x^4 + 588*x^5 - 1578*x^6 - 11511*x^7 +...
A(x)^4 = 1 + 4*x - 6*x^2 - 56*x^3 + 87*x^4 + 1008*x^5 - 1578*x^6 - 20464*x^7 +...
Note that a bisection of A^4 equals a bisection of A^3.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A143045, A143047, A143048, A143049, A213252, A213281, A213335.

Cf. A171200.

Programs

PARI

a(n)=local(A=x+x*O(x^n));for(i=0,n,A=1+x*subst(A,x,-x)^3);polcoeff(A,n)

Formula

G.f. satisfies: A(x) = 1 + x*(1 - x*A(x)^3)^3.

G.f. satisfies: [A(x)^4 + A(-x)^4]/2 = [A(x)^3 + A(-x)^3]/2.

a(0) = 1; a(n) = (-1)^(n-1) * Sum_{i, j, k>=0 and i+j+k=n-1} a(i) * a(j) * a(k). - Seiichi Manyama, Jul 08 2025