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A110634 Every 2nd term of A083946 where the self-convolution 2nd power is congruent modulo 4 to A083946, which consists entirely of numbers 1 through 6. 2

%I

%S 1,3,3,6,3,6,6,3,6,3,6,3,6,3,6,2,6,6,6,3,6,4,6,6,4,3,3,6,3,3,3,3,6,2,

%T 3,3,1,6,6,2,6,6,3,3,6,1,6,6,6,3,6,6,3,6,1,6,6,2,3,6,6,3,3,4,6,6,2,3,

%U 6,4,3,6,2,6,3,6,3,6,2,6,6,4,3,3,2,3,3,6,3,3,5,3,3,2,6,6,2,3,6,1,3,3,5,3,6

%N Every 2nd term of A083946 where the self-convolution 2nd power is congruent modulo 4 to A083946, which consists entirely of numbers 1 through 6.

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

%e A(x)^2 = 1 + 6*x + 15*x^2 + 30*x^3 + 51*x^4 + 66*x^5 +...

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

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

%e where G(x) is the g.f. of A083946.

%o (PARI) {a(n)=local(d=2,m=6,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. A110632, A110633.

%K nonn

%O 0,2

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

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Last modified November 22 16:31 EST 2019. Contains 329396 sequences. (Running on oeis4.)