A196308 A trisection of A196306.

1, 1, -1, -1, -1, 0, -1, 1, -1, 0, -1, -1, 0, 1, -1, -1, 1, 0, 1, 0, -1, 0, -1, -1, 1, -1, 0, 0, 1, -1, -1, -1, -1, 0, -1, 0, 1, 0, -1, 0, 0, 0, -1, 0, 1, -1, -1, 1, -1, -1, 0, -1, 0, -1, -1, 1, -1, -1, 1, 0, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 0, 1, -1, -1, -1, -1, 0, 0, 0, 0, 1, 0, 1, -1, -1, -1, -1, 1, 0, -1, -1

Offset

0

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.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..333

Example

G.f.: A(x) = 1 + x - x^2 - x^3 - x^4 - x^6 + x^7 - x^8 - x^10 - x^11 + x^13 - x^14 - x^15 + x^16 + x^18 - x^20 - x^22 - x^23 + x^24 - x^25 + x^28 - x^29 - x^30 - x^31 - x^32 - x^34 + x^36 - x^38 - x^42 + x^44 - x^45 - x^46 + x^47 - x^48 - x^49 - x^51 - x^53 - x^54 + x^55 - x^56 - x^57 + x^58 - x^60 - x^61 + x^62 - x^63 - x^64 + x^65 + x^66 + x^67 - x^68 + x^69 - x^70 + x^71 + x^73 - x^74 - x^75 - x^76 - x^77 + x^82 + x^84 - x^85 - x^86 - x^87 - x^88 + x^89 - x^91 - x^92 +...
where the following series consists entirely of integer coefficients:
(A(x^3) + 3*x)^(1/3) =  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 + 21178*x^13 - 59509*x^14 + 168401*x^15 - 479477*x^16 + 1372536*x^17 - 3947678*x^18 + 11402376*x^19 - 33059314*x^20 + 96177750*x^21 +...+ A196307(n)*x^n +...

Prog

(PARI) {a(n)=local(A=1+3*x); if(n==0, 1, for(j=1, 3*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^(3*n)), 3*n))}

Crossrefs

Cf. A196306, A196307.

Sequence in context: A378442 A373851 A142720 * A091862 A351564 A237048

Adjacent sequences: A196305 A196306 A196307 * A196309 A196310 A196311

Keyword

sign

Author

Paul D. Hanna, Oct 01 2011

Status

approved