A106219 Self-convolution cube-root of A106216, which consists entirely of digits {0,1,2} after the initial terms {1,3}.
1, 1, -1, 2, -4, 9, -21, 53, -137, 362, -971, 2642, -7272, 20211, -56631, 159795, -453650, 1294797, -3713100, 10693036, -30910440, 89657680, -260860962, 761114168, -2226409022, 6528039545, -19182376302, 56479676608, -166605140314, 492304708589, -1457061274821, 4318906269671
Offset: 0
Keywords
Examples
A(x) = 1 + x - x^2 + 2*x^3 - 4*x^4 + 9*x^5 - 21*x^6 + 53*x^7 -+...
A(x)^3 = 1 + 3*x + x^3 + 2*x^6 + 2*x^9 + 2*x^12 + 2*x^21 + x^24 +...
A106216 = {1,3,0,1,0,0,2,0,0,2,0,0,2,0,0,0,0,0,0,0,0,2,0,0,1,...}.
Programs
-
PARI
{a(n)=local(A=1+3*x);if(n==0,1, for(j=1,n, for(k=0,2,t=polcoeff((A+k*x^j+x*O(x^j))^(1/3),j); if(denominator(t)==1,A=A+k*x^j;break))); return(polcoeff((A+x*O(x^n))^(1/3),n)))}
Formula
Limit a(n+1)/a(n) = -3.09744345956297443415996844224370585278444314...