A196307 The cube of the g.f. equals the g.f. of A196306.

1, 1, -1, 2, -4, 9, -22, 55, -142, 375, -1009, 2753, -7599, 21178, -59509, 168401, -479477, 1372536, -3947678, 11402376, -33059314, 96177750, -280671373, 821379083, -2409938978, 7087502564, -20889306810, 61691675424, -182531101523, 541000651928, -1606046079955, 4774977156350

Offset: 0

Author

Paul D. Hanna, Oct 01 2011

Keywords

• sign

Comments

A196306 is defined as the Coefficients in the g.f. C(x), where -1 <= A196306(n) <= 1 for all n>1 with initial terms {1,3}, such that C(x)^(1/3) consists entirely of integer coefficients.

Limit a(n+1)/a(n) = -3.1069369226 1299813830 3346689095 3281527516 0860761416 4775926338 8951561634 ...

Examples

			G.f.: A(x) = 1 + x - x^2 + 2*x^3 - 4*x^4 + 9*x^5 - 22*x^6 + 55*x^7 - 142*x^8 + 375*x^9 - 1009*x^10 + 2753*x^11 - 7599*x^12 +...
where
A(x)^3 = 1 + 3*x + x^3 - x^6 - x^9 - x^12 - x^18 + x^21 - x^24 - x^30 - x^33 + x^39 - x^42 - x^45 + x^48 +...+ A196306(n)*x^n +...
A196306 begins: [1,3,0,1,0,0,-1,0,0,-1,0,0,-1,0,0,0,0,0,-1,0,0,1,0,0,-1,...].
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A196306, A196308, A106219 (variant).

Programs

PARI

{a(n)=local(A=1+3*x); if(n==0, 1, for(j=1, n, for(k=-1, 1, t=polcoeff((A+k*x^j+x*O(x^j))^(1/3), j);
if(denominator(t)==1, A=A+k*x^j; break))); polcoeff((A+x*O(x^n))^(1/3), n))}