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Trisection of A083953 such that the self-convolution cube is congruent modulo 9 to A083953, which consists entirely of 1's, 2's and 3's.
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%I #5 Mar 30 2012 18:36:50

%S 1,1,3,3,1,2,2,1,2,3,2,3,3,2,2,3,2,1,2,1,1,1,1,1,3,1,1,3,1,3,1,2,1,3,

%T 1,3,1,1,1,2,2,3,3,2,3,1,2,1,3,3,2,3,3,1,2,3,3,1,3,3,2,2,2,1,2,3,3,3,

%U 3,1,2,2,3,2,1,2,2,1,2,3,3,2,2,1,1,2,1,3,2,2,2,1,3,2,2,3,3,2,3,1,1,1,1,3,3

%N Trisection of A083953 such that the self-convolution cube is congruent modulo 9 to A083953, which consists entirely of 1's, 2's and 3's.

%C Congruent modulo 3 to A084203 and A104405; the self-convolution cube of A084203 equals A083953.

%F a(n) = A083953(3*n) for n>=0. G.f. satisfies: A(x^3) = G(x) - 3*x*(1+x)/(1-x^3), where G(x) is the g.f. of A083953. G.f. satisfies: A(x)^3 = A(x^3) + 3*x*(1+x)/(1-x^3) + 9*x^2*H(x) where H(x) is the g.f. of A111582.

%o (PARI) {a(n)=local(p=3,A,C,X=x+x*O(x^(p*n)));if(n==0,1, A=sum(i=0,n-1,a(i)*x^(p*i))+p*x*((1-x^(p-1))/(1-X))/(1-X^p); for(k=1,p,C=polcoeff((A+k*x^(p*n))^(1/p),p*n); if(denominator(C)==1,return(k);break)))}

%Y Cf. A083953, A111582, A084203, A104405.

%K nonn

%O 0,3

%A _Robert G. Wilson v_ and _Paul D. Hanna_, Aug 08 2005