A110648 Every third term of A084067 where the self-convolution third power is congruent modulo 9 to A084067, which consists entirely of numbers 1 through 12.
1, 4, 4, 8, 6, 12, 8, 12, 12, 12, 10, 12, 2, 8, 12, 4, 8, 8, 4, 4, 9, 4, 4, 12, 2, 12, 6, 8, 7, 4, 8, 12, 12, 8, 12, 8, 2, 8, 2, 8, 3, 12, 4, 12, 4, 12, 2, 12, 9, 12, 6, 12, 10, 8, 6, 12, 12, 12, 2, 8, 9, 12, 10, 12, 2, 8, 2, 4, 5, 4, 6, 12, 12, 8, 2, 12, 9, 4, 8, 4, 8, 12, 8, 4, 10, 8, 8, 12, 1, 12
Offset: 0
Keywords
Examples
A(x) = 1 + 4*x + 4*x^2 + 8*x^3 + 6*x^4 + 12*x^5 +... A(x)^3 = 1 + 12*x + 60*x^2 + 184*x^3 + 450*x^4 + 948*x^5 +... A(x)^3 (mod 9) = 1 + 3*x + 6*x^2 + 4*x^3 + 3*x^5 + 4*x^6 +... G(x) = 1 + 12*x + 6*x^2 + 4*x^3 + 9*x^4 + 12*x^5 + 4*x^6 +... where G(x) is the g.f. of A084067.
Programs
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PARI
{a(n)=local(d=3,m=12,A=1+m*x); for(j=2,d*n, for(k=1,m,t=polcoeff((A+k*x^j+x*O(x^j))^(1/m),j); if(denominator(t)==1,A=A+k*x^j;break)));polcoeff(A,d*n)}