cp's OEIS Frontend

A110649 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.

%I A110649 #7 Mar 10 2015 02:07:02
%S A110649 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 A110649 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 A110649 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 A110649 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 A110649 A(x) = 1 + 6*x + 9*x^2 + 4*x^3 + 12*x^4 + 6*x^5 +...
%e A110649 A(x)^2 = 1 + 12*x + 54*x^2 + 116*x^3 + 153*x^4 + 228*x^5 +...
%e A110649 A(x)^2 (mod 8) = 1 + 4*x + 6*x^2 + 4*x^3 + x^4 + 4*x^5 +...
%e A110649 G(x) = 1 + 12*x + 6*x^2 + 4*x^3 + 9*x^4 + 12*x^5 + 4*x^6 +...
%e A110649 where G(x) is the g.f. of A084067.
%o A110649 (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 A110649 Cf. A084067, A110645, A110646, A110647, A110648.
%K A110649 nonn
%O A110649 0,2
%A A110649 _Robert G. Wilson v_ and _Paul D. Hanna_, Aug 30 2005