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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
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
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
Sequence in context: A050306 A205453 A328776 * A119979 A143149 A268498
KEYWORD
nonn
AUTHOR
STATUS
approved