%I #7 Mar 10 2015 02:07:28
%S 1,5,10,5,10,3,5,10,10,10,5,5,5,5,5,8,10,10,5,10,7,10,5,10,5,7,5,5,10,
%T 10,7,10,10,5,5,9,5,5,5,10,8,10,10,10,10,8,5,5,10,10,5,10,10,10,5,6,5,
%U 5,10,5,10,10,5,10,10,1,5,5,10,10,5,5,5,10,5,5,10,5,5,10,4,10,10,5,5,6,10
%N Every 2nd term of A083950 where the self-convolution 2nd power is congruent modulo 4 to A083950, which consists entirely of numbers 1 through 10.
%e A(x) = 1 + 5*x + 10*x^2 + 5*x^3 + 10*x^4 + 3*x^5 + 5*x^6 +...
%e A(x)^2 = 1 + 10*x + 45*x^2 + 110*x^3 + 170*x^4 + 206*x^5 +...
%e A(x)^2 (mod 4) = 1 + 2*x + x^2 + 2*x^3 + 2*x^4 + 2*x^5 +...
%e G(x) = 1 + 10*x + 5*x^2 + 10*x^3 + 10*x^4 + 2*x^5 + 5*x^6 +...
%e where G(x) is the g.f. of A083950.
%o (PARI) {a(n)=local(d=2,m=10,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. A083950, A110641, A110642.
%K nonn
%O 0,2
%A _Robert G. Wilson v_ and _Paul D. Hanna_, Aug 30 2005