cp's OEIS Frontend

A110633 Every third term of A083946 where the self-convolution third power is congruent modulo 9 to A083946, which consists entirely of numbers 1 through 6.

%I A110633 #8 Jan 15 2022 23:04:42
%S A110633 1,2,6,4,6,4,3,2,6,4,2,6,6,4,4,2,4,2,6,4,3,4,2,6,1,4,2,2,3,4,1,6,6,2,
%T A110633 6,6,1,6,2,6,6,2,4,6,2,4,4,4,2,6,6,2,2,6,4,4,2,6,6,4,5,4,2,6,2,4,1,2,
%U A110633 5,2,3,4,6,6,6,6,2,4,5,2,3,2,1,2,4,2,5,2,4,2,6,2,2,4,4,4,3,2,1,2,6,6,2,6,3
%N A110633 Every third term of A083946 where the self-convolution third power is congruent modulo 9 to A083946, which consists entirely of numbers 1 through 6.
%e A110633 A(x) = 1 + 2*x + 6*x^2 + 4*x^3 + 6*x^4 + 4*x^5 + 3*x^6 + ...
%e A110633 A(x)^3 = 1 + 6*x + 30*x^2 + 92*x^3 + 246*x^4 + 492*x^5 + ...
%e A110633 A(x)^3 (mod 9) = 1 + 6*x + 3*x^2 + 2*x^3 + 3*x^4 + 6*x^5 + ...
%e A110633 G(x) = 1 + 6*x + 3*x^2 + 2*x^3 + 3*x^4 + 6*x^5 + ...
%e A110633 where G(x) is the g.f. of A083946.
%o A110633 (PARI) {a(n)=local(d=3,m=6,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 A110633 Cf. A083946, A110632, A110634.
%K A110633 nonn
%O A110633 0,2
%A A110633 _Robert G. Wilson v_ and _Paul D. Hanna_, Aug 30 2005