|
%I #7 Mar 14 2015 10:00:46
%S 1,2,7,4,3,2,1,8,6,6,6,4,4,2,8,8,7,6,8,6,8,6,7,8,3,4,3,6,3,8,1,4,4,8,
%T 3,6,6,2,5,8,1,4,6,4,6,6,1,8,1,6,5,8,4,4,8,4,5,8,5,2,4,8,6,4,5,2,8,8,
%U 7,4,6,4,5,8,6,8,6,4,5,4,8,4,4,4,7,8,4,2,1,8,3,4,7,2,7,8,4,6,6,4,8,6,7,6,4
%N Every 4th term of A083948 where the self-convolution 4th power is congruent modulo 16 to A083948, which consists entirely of numbers 1 through 8.
%e A(x) = 1 + 2*x + 7*x^2 + 4*x^3 + 3*x^4 + 2*x^5 + x^6 +...
%e A(x)^4 = 1 + 8*x + 52*x^2 + 216*x^3 + 754*x^4 + 2008*x^5 +...
%e A(x)^4 (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=4,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, A110638.
%K nonn
%O 0,2
%A _Robert G. Wilson v_ and _Paul D. Hanna_, Aug 30 2005
|
