A110648 - OEIS

%I #6 Mar 30 2012 18:36:50

%S 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,

%T 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,

%U 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

%N 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.

%e A(x) = 1 + 4*x + 4*x^2 + 8*x^3 + 6*x^4 + 12*x^5 +...

%e A(x)^3 = 1 + 12*x + 60*x^2 + 184*x^3 + 450*x^4 + 948*x^5 +...

%e A(x)^3 (mod 9) = 1 + 3*x + 6*x^2 + 4*x^3 + 3*x^5 + 4*x^6 +...

%e G(x) = 1 + 12*x + 6*x^2 + 4*x^3 + 9*x^4 + 12*x^5 + 4*x^6 +...

%e where G(x) is the g.f. of A084067.

%o (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)}

%Y Cf. A084067, A110645, A110646, A110647, A110649.

%K nonn

%O 0,2

%A _Robert G. Wilson v_ and _Paul D. Hanna_, Aug 30 2005