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A094423 A045873(n)^2. 1
1, 4, 1, 144, 361, 484, 19321, 28224, 128881, 2427364, 1745041, 26501904, 285643801, 64995844, 4675961161, 31354493184, 149793121, 741117817924, 3178942795681, 545370434064, 107989070784841, 292105630845604 (list; graph; refs; listen; history; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

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

FORMULA

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.

CROSSREFS

Sequence in context: A164797 A152841 A125083 * A094337 A038019 A164804

Adjacent sequences:  A094420 A094421 A094422 * A094424 A094425 A094426

KEYWORD

nonn

AUTHOR

Ralf Stephan, May 04 2004

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Last modified February 17 14:50 EST 2012. Contains 206050 sequences.