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A110627
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Bisection of A083952 such that the self-convolution is congruent modulo 4 to A083952, which consists entirely of 1's and 2's.
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1
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1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Congruent modulo 2 to A084202 and A108336; the self-convolution of A084202 equals A083952.
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FORMULA
| a(n) = A083952(2*n) for n>=0. G.f. satisfies: A(x^2) = G(x) - 2*x/(1-x^2), where G(x) is the g.f. of A083952. G.f. satisfies: A(x)^2 = A(x^2) + 2*x/(1-x^2) + 4*x^2*H(x) where H(x) is the g.f. of A111581.
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PROG
| (PARI) {a(n)=local(p=2, 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)))}
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CROSSREFS
| Cf. A083952, A111581, A084202, A108336.
Sequence in context: A047895 A178474 A164822 * A205107 A087187 A029380
Adjacent sequences: A110624 A110625 A110626 * A110628 A110629 A110630
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KEYWORD
| nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com) and Paul D. Hanna (pauldhanna(AT)juno.com), Aug 08 2005
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