A106225 Self-convolution 6th power equals A106224, which consists entirely of digits {0,1,2,3,4,5} after the initial terms {1,6}.

1, 1, -2, 7, -27, 114, -506, 2322, -10919, 52316, -254369, 1251563, -6218656, 31153743, -157167147, 797682007, -4069817562, 20860266354, -107358128720, 554533772363, -2873667741743, 14935575580894, -77833224795929, 406595414780038, -2128748177726089, 11167899337858904

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Formula

Limit a(n+1)/a(n) = -5.502856676359094846755190514140489974645...

Example

A(x) = 1 + x - 2*x^2 + 7*x^3 - 27*x^4 + 114*x^5 - 506*x^6 +-...
A(x)^6 = 1 + 6*x + 3*x^2 + 2*x^3 + 3*x^4 + 3*x^8 + 4*x^9 +...
A106224 = {1,6,3,2,3,0,0,0,3,4,3,0,0,0,3,2,0,0,0,0,3,2,...}.

Prog

(PARI) {a(n)=local(A=1+6*x); if(n==0, 1, for(j=1, n, for(k=0, 5, t=polcoeff((A+k*x^j+x*O(x^j))^(1/6), j); if(denominator(t)==1, A=A+k*x^j; break))); return(polcoeff((A+x*O(x^n))^(1/6), n)))}

Crossrefs

Cf. A106224, A106219, A106221, A106223, A106227.

Sequence in context: A150626 A150627 A150628 * A127897 A180473 A011965

Adjacent sequences: A106222 A106223 A106224 * A106226 A106227 A106228

Keyword

sign,base

Author

Paul D. Hanna, May 01 2005

Status

approved