1,2

The g.f. is an example of a rational function with nonnegative integer coefficients that is not N-rational.

Ira Gessel, Rational functions with nonnegative power series, (slides).

G.f.: (x+5x^2)/(1+x-5x^2-125x^3).

a(n) = 1/16*[2*5^n - (1+2I)^(2n) - (1-2I)^(2n)] = 1/4*[Im(1+2I)^n]^2 = 5^n/4*sin[n*arctan(2)]^2.

Sequence in context: A164797 A152841 A125083 this_sequence A094337 A038019 A164804

Adjacent sequences: A094420 A094421 A094422 this_sequence A094424 A094425 A094426

nonn

Ralf Stephan, May 04 2004