A110647 Every 4th term of A084067 where the self-convolution 4th power is congruent modulo 8 to A084067, which consists entirely of numbers 1 through 12.

1, 9, 12, 6, 12, 9, 12, 6, 6, 2, 6, 12, 8, 3, 12, 9, 6, 12, 2, 3, 3, 7, 9, 9, 12, 3, 3, 2, 12, 6, 3, 9, 3, 4, 6, 3, 9, 6, 3, 10, 6, 9, 12, 9, 12, 9, 9, 6, 2, 9, 12, 5, 3, 6, 12, 9, 6, 9, 12, 6, 8, 6, 12, 10, 9, 12, 1, 9, 3, 9, 12, 6, 7, 12, 12, 2, 9, 3, 9, 12, 12, 4, 9, 9, 11, 6, 6, 1, 9, 6, 10, 3, 12

Offset

0,2

Links

Table of n, a(n) for n=0..92.

Example

A(x) = 1 + 9*x + 12*x^2 + 6*x^3 + 12*x^4 + 9*x^5 +...
A(x)^4 = 1 + 36*x + 534*x^2 + 4236*x^3 + 19785*x^4 +...
A(x)^4 (mod 8) = 1 + 4*x + 6*x^2 + 4*x^3 + x^4 + 4*x^5 +...
G(x) = 1 + 12*x + 6*x^2 + 4*x^3 + 9*x^4 + 12*x^5 + 4*x^6 +...
where G(x) is the g.f. of A084067.

Prog

(PARI) {a(n)=local(d=4, m=12, A=1+m*x); for(j=2, d*n, for(k=1, m, t=polcoeff((A+k*x^j+x*O(x^j))^(1/m), j); if(denominator(t)==1, A=A+k*x^j; break))); polcoeff(A, d*n)}

Crossrefs

Cf. A084067, A110645, A110646, A110648, A110649.

Sequence in context: A196509 A269026 A124606 * A347943 A335168 A295486

Adjacent sequences: A110644 A110645 A110646 * A110648 A110649 A110650

Keyword

nonn

Author

Robert G. Wilson v and Paul D. Hanna, Aug 30 2005

Status

approved