cp's OEIS Frontend

A110629 Every 4th term of A083954 such that the self-convolution 4th power is congruent modulo 8 to A083954, which consists entirely of numbers 1 through 4.

%I A110629 #7 Mar 14 2015 10:00:31
%S A110629 1,3,1,3,3,2,4,3,2,3,3,4,2,2,2,1,1,4,1,3,4,3,2,2,1,1,3,4,1,1,2,3,2,2,
%T A110629 3,4,4,1,4,4,1,4,2,3,1,2,1,4,3,3,1,4,3,3,2,3,4,2,3,4,1,2,1,3,4,3,4,1,
%U A110629 4,2,2,3,1,4,3,2,1,4,3,4,4,2,1,4,1,4,4,2,4,4,1,3,3,4,1,1,1,4,3,2,1,3,1,2,2
%N A110629 Every 4th term of A083954 such that the self-convolution 4th power is congruent modulo 8 to A083954, which consists entirely of numbers 1 through 4.
%F A110629 a(n) = A083954(4*n) for n>=0.
%e A110629 A(x) = 1 + 3*x + x^2 + 3*x^3 + 3*x^4 + 2*x^5 + 4*x^6 + ...
%e A110629 A(x)^4 = 1 + 12*x + 58*x^2 + 156*x^3 + 315*x^4 + 620*x^5 +...
%e A110629 A(x)^4 (mod 8) = 1 + 4*x + 2*x^2 + 4*x^3 + 3*x^4 + 4*x^5 +...
%e A110629 G083954(x) = 1 + 4*x + 2*x^2 + 4*x^3 + 3*x^4 + 4*x^5 +...
%e A110629 where G083954(x) is the g.f. of A083954.
%o A110629 (PARI) {a(n)=local(d=4,m=4,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 A110629 Cf. A083954, A110630.
%K A110629 nonn
%O A110629 0,2
%A A110629 _Robert G. Wilson v_ and _Paul D. Hanna_, Aug 09 2005