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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, 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 (list; graph; refs; listen; history; text; internal format)
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: A073067 A003637 A317413 * 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

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Last modified December 12 17:33 EST 2019. Contains 329960 sequences. (Running on oeis4.)