|
%I #7 Mar 12 2015 20:00:36
%S 1,7,3,1,6,6,4,8,7,8,8,7,3,3,3,1,4,3,6,5,1,6,6,1,1,5,4,8,5,5,4,6,5,8,
%T 7,6,5,6,6,5,8,4,7,4,1,3,7,7,4,6,8,7,4,8,8,1,5,3,5,5,6,2,4,4,7,2,6,2,
%U 1,4,3,5,5,3,5,1,5,3,7,8,6,5,1,2,1,1,2,4,6,1,6,3,5,1,7,3,4,2,6,7,1,3,1,8,3
%N Every 8th term of A083948 where the self-convolution 8th power is congruent modulo 16 to A083948, which consists entirely of numbers 1 through 8.
%e A(x) = 1 + 7*x + 3*x^2 + x^3 + 6*x^4 + 6*x^5 + 4*x^6 + 8*x^7 +...
%e A(x)^8 = 1 + 56*x + 1396*x^2 + 20392*x^3 + 193458*x^4 +...
%e A(x)^8 (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=8,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, A110632, A110633.
%K nonn
%O 0,2
%A _Robert G. Wilson v_ and _Paul D. Hanna_, Aug 30 2005
|
