A110627 Bisection of A083952 such that the self-convolution is congruent modulo 4 to A083952, which consists entirely of 1's and 2's.

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

Offset: 0

Author

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

Keywords

• nonn

Comments

Congruent modulo 2 to A084202 and A108336; the self-convolution of A084202 equals A083952.

Crossrefs

Cf. A083952, A111581, A084202, A108336.

Programs

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)))}

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.