A110629 Every 4th term of A083954 such that the self-convolution 4th power is congruent modulo 8 to A083954, which consists entirely of numbers 1 through 4.

1, 3, 1, 3, 3, 2, 4, 3, 2, 3, 3, 4, 2, 2, 2, 1, 1, 4, 1, 3, 4, 3, 2, 2, 1, 1, 3, 4, 1, 1, 2, 3, 2, 2, 3, 4, 4, 1, 4, 4, 1, 4, 2, 3, 1, 2, 1, 4, 3, 3, 1, 4, 3, 3, 2, 3, 4, 2, 3, 4, 1, 2, 1, 3, 4, 3, 4, 1, 4, 2, 2, 3, 1, 4, 3, 2, 1, 4, 3, 4, 4, 2, 1, 4, 1, 4, 4, 2, 4, 4, 1, 3, 3, 4, 1, 1, 1, 4, 3, 2, 1, 3, 1, 2, 2

Offset

0,2

Links

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

Formula

a(n) = A083954(4*n) for n>=0.

Example

A(x) = 1 + 3*x + x^2 + 3*x^3 + 3*x^4 + 2*x^5 + 4*x^6 + ...
A(x)^4 = 1 + 12*x + 58*x^2 + 156*x^3 + 315*x^4 + 620*x^5 +...
A(x)^4 (mod 8) = 1 + 4*x + 2*x^2 + 4*x^3 + 3*x^4 + 4*x^5 +...
G083954(x) = 1 + 4*x + 2*x^2 + 4*x^3 + 3*x^4 + 4*x^5 +...
where G083954(x) is the g.f. of A083954.

Prog

(PARI) {a(n)=local(d=4, m=4, 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. A083954, A110630.

Sequence in context: A050306 A205453 A328776 * A119979 A143149 A268498

Adjacent sequences: A110626 A110627 A110628 * A110630 A110631 A110632

Keyword

nonn

Author

Robert G. Wilson v and Paul D. Hanna, Aug 09 2005

Status

approved