A110630 Every 2nd term of A083954 such that the self-convolution 2nd power is congruent modulo 8 to A083954, which consists entirely of numbers 1 through 4.

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

Offset

0,2

Links

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

Formula

a(n) = A083954(2*n) for n>=0.

Example

A(x) = 1 + 2*x + 3*x^2 + 4*x^3 + x^4 + 4*x^5 + 3*x^6 + 4*x^7 +...
A(x)^2 = 1 + 4*x + 10*x^2 + 20*x^3 + 27*x^4 + 36*x^5 + 44*x^6 +...
A(x)^2 (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 + 4*x^6 +...
where G083954(x) is the g.f. of A083954.

Prog

(PARI) {a(n)=local(d=2, 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, A110629.

Sequence in context: A327464 A318308 A003324 * A343321 A238883 A363126

Adjacent sequences: A110627 A110628 A110629 * A110631 A110632 A110633

Keyword

nonn

Author

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

Status

approved