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%I #7 Mar 10 2015 02:07:51
%S 1,4,2,4,7,8,4,8,3,8,2,8,1,8,8,8,6,4,6,4,6,8,4,8,4,8,2,8,8,8,8,8,7,8,
%T 6,8,8,4,6,4,8,8,6,8,7,4,8,4,3,4,4,4,3,8,6,8,3,8,8,8,1,8,4,8,4,8,8,8,
%U 3,8,6,8,6,8,2,8,5,8,8,8,1,8,4,8,6,4,4,4,6,8,6,8,1,4,8,4,1,8,6,8,5,4,8,4,4
%N Every 2nd term of A083948 where the self-convolution 2nd power is congruent modulo 16 to A083948, which consists entirely of numbers 1 through 8.
%e A(x) = 1 + 4*x + 2*x^2 + 4*x^3 + 7*x^4 + 8*x^5 + 4*x^6 +...
%e A(x)^2 = 1 + 8*x + 20*x^2 + 24*x^3 + 50*x^4 + 88*x^5 +...
%e A(x)^2 (mod 16) = 1 + 8*x + 4*x^2 + 8*x^3 + 2*x^4 + 8*x^5 +...
%e G(x) = 1 + 8*x + 4*x^2 + 8*x^3 + 2*x^4 + 8*x^5 + 4*x^6 +...
%e where G(x) is the g.f. of A083948.
%o (PARI) {a(n)=local(d=2,m=8,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. A083948, A110636, A110637.
%K nonn
%O 0,2
%A _Robert G. Wilson v_ and _Paul D. Hanna_, Aug 30 2005
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