

A110628


Trisection of A083953 such that the selfconvolution 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
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OFFSET

0,3


COMMENTS

Congruent modulo 3 to A084203 and A104405; the selfconvolution 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)/(1x^3), where G(x) is the g.f. of A083953. G.f. satisfies: A(x)^3 = A(x^3) + 3*x*(1+x)/(1x^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, n1, a(i)*x^(p*i))+p*x*((1x^(p1))/(1X))/(1X^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



