A110635 Every 7th term of A083947 such that the self-convolution 7th power is congruent modulo 49 to A083947, which consists entirely of numbers 1 through 7.

1, 1, 5, 1, 1, 4, 2, 1, 1, 3, 5, 1, 2, 5, 1, 7, 6, 4, 4, 6, 4, 5, 7, 3, 4, 2, 4, 3, 3, 2, 7, 4, 6, 6, 3, 1, 1, 6, 5, 6, 6, 3, 1, 2, 5, 7, 3, 3, 7, 5, 5, 6, 4, 6, 3, 4, 2, 5, 4, 4, 7, 3, 4, 1, 5, 6, 7, 2, 2, 5, 4, 1, 4, 4, 1, 1, 4, 3, 6, 7, 6, 2, 6, 6, 2, 1, 6, 6, 1, 5, 2, 2, 5, 5, 4, 2, 3, 7, 4, 5, 1, 3, 6, 4, 4

Offset

0,3

Comments

Congruent modulo 7 to A084207, where the self-convolution 7th power of A084207 equals A083947.

Links

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

Formula

a(n) = A083947(7*n) for n>=0.

G.f. satisfies: A(x^7) = G(x) - 7*x*((1-x^6)/(1-x))/(1-x^7), where G(x) is the g.f. of A083947.

G.f. satisfies: A(x)^7 = A(x^7) + 7*x*((1-x^6)/(1-x))/(1-x^7) + 49*x^2*H(x) where H(x) is the g.f. of A111584.

Prog

(PARI) {a(n)=local(p=7, 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. A083947, A111584, A084207.

Sequence in context: A260210 A139391 A196612 * A179773 A244977 A071170

Adjacent sequences: A110632 A110633 A110634 * A110636 A110637 A110638

Keyword

nonn

Author

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

Status

approved