A110628 - OEIS

A110628

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.

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, 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, 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

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OFFSET

0,3

COMMENTS

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

LINKS

Table of n, a(n) for n=0..104.

FORMULA

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.

PROG

(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)))}

CROSSREFS

Cf. A083953, A111582, A084203, A104405.

Sequence in context: A003637 A317413 A359838 * A107292 A225331 A004550

Adjacent sequences: A110625 A110626 A110627 * A110629 A110630 A110631

KEYWORD

nonn

AUTHOR

Robert G. Wilson v and Paul D. Hanna, Aug 08 2005

STATUS

approved