A083350 Integer coefficients of a power series A(x) such that A(x)^3 = A083349(x).

1, 1, 1, -1, 3, 0, -6, 17, -17, -19, 114, -215, 111, 609, -2084, 2947, 1187, -16252, 38872, -32709, -87431, 390618, -673709, 47692, 3018098, -8616766, 9761812, 13605710, -84546525, 171930010, -77194029, -610108400, 2090199824, -2940478260, -1840404119, 19501756943, -46202080484

Offset

0,5

Comments

Self-convolution cube equals A083349.

A083349 is the minimal permutation of the positive integers having a self-convolution cube-root consisting entirely of integers.

Links

Table of n, a(n) for n=0..36.

N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

Example

A083349(x)^(1/3) = A(x) = 1 + x + x^2 - x^3 + 3x^4 + 0x^5 - 6x^6 + ...

Mathematica

n = 40; A = 1 + 3x; P = Table[0, 3(n+1)]; P[[1]] = 1; P[[3]] = 2; For[j = 2, j <= n, j++, For[k = 2, k <= 3(n+1), k++, If[P[[k]] == 0, t = Coefficient[(A + k x^j + x^2 O[x]^j)^(1/3), x, j]; If[Denominator[t] == 1, P[[k]] = j+1; A = A + k x^j; Break[]]]]];
CoefficientList[A^(1/3) + O[x]^n, x] (* Jean-François Alcover, Jul 26 2018, from PARI *)

Prog

(PARI) {a(n)=local(A=1+3*x, P=vector(3*(n+1))); P[1]=1; P[3]=2; for(j=2, n, for(k=2, 3*(n+1), if(P[k]==0, t=polcoeff((A+k*x^j+x^2*O(x^j))^(1/3), j); if(denominator(t)==1, P[k]=j+1; A=A+k*x^j; break)))); return(polcoeff((A+x*O(x^n))^(1/3), n))}

Crossrefs

Cf. A083349, A106213, A106214.

Sequence in context: A019145 A059684 A270509 * A002043 A171002 A375987

Adjacent sequences: A083347 A083348 A083349 * A083351 A083352 A083353

Keyword

sign

Author

Paul D. Hanna, Apr 25 2003; revised May 01 2005

Status

approved