A110649 - OEIS

%I #7 Mar 10 2015 02:07:02

%S 1,6,9,4,12,6,6,12,12,8,9,12,12,6,6,10,6,12,2,6,6,12,12,12,8,12,3,4,

%T 12,12,9,6,6,4,12,12,2,6,3,6,3,6,7,6,9,8,9,12,12,12,3,12,3,6,2,6,12,2,

%U 6,6,3,12,9,4,3,12,4,12,6,2,3,12,9,6,6,6,3,6,10,6,6,6,9,6,12,12,9,2,12,6,9

%N Every 2nd term of A084067 where the self-convolution 2nd power is congruent modulo 8 to A084067, which consists entirely of numbers 1 through 12.

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

%e A(x)^2 = 1 + 12*x + 54*x^2 + 116*x^3 + 153*x^4 + 228*x^5 +...

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

%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=2,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, A110648.

%K nonn

%O 0,2

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