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 A110647 Every 4th term of A084067 where the self-convolution 4th power is congruent modulo 8 to A084067, which consists entirely of numbers 1 through 12. 4

%I #7 Mar 14 2015 10:01:01

%S 1,9,12,6,12,9,12,6,6,2,6,12,8,3,12,9,6,12,2,3,3,7,9,9,12,3,3,2,12,6,

%T 3,9,3,4,6,3,9,6,3,10,6,9,12,9,12,9,9,6,2,9,12,5,3,6,12,9,6,9,12,6,8,

%U 6,12,10,9,12,1,9,3,9,12,6,7,12,12,2,9,3,9,12,12,4,9,9,11,6,6,1,9,6,10,3,12

%N Every 4th term of A084067 where the self-convolution 4th power is congruent modulo 8 to A084067, which consists entirely of numbers 1 through 12.

%e A(x) = 1 + 9*x + 12*x^2 + 6*x^3 + 12*x^4 + 9*x^5 +...

%e A(x)^4 = 1 + 36*x + 534*x^2 + 4236*x^3 + 19785*x^4 +...

%e A(x)^4 (mod 8) = 1 + 4*x + 6*x^2 + 4*x^3 + x^4 + 4*x^5 +...

%e G(x) = 1 + 12*x + 6*x^2 + 4*x^3 + 9*x^4 + 12*x^5 + 4*x^6 +...

%e where G(x) is the g.f. of A084067.

%o (PARI) {a(n)=local(d=4,m=12,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. A084067, A110645, A110646, A110648, A110649.

%K nonn

%O 0,2

%A _Robert G. Wilson v_ and _Paul D. Hanna_, Aug 30 2005

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Last modified June 25 10:28 EDT 2024. Contains 373701 sequences. (Running on oeis4.)