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A094423 A045873(n)^2. 2
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; text; 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

Table of n, a(n) for n=1..22.

Ira M. Gessel, Rational Functions With Nonnegative Integer Coefficients, slides, 50th Séminaire Lotharingien de Combinatoire, 2003.

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.

PROG

(PARI) Vec((x+5*x^2)/(1+x-5*x^2-125*x^3) + O(x^30)) \\ Michel Marcus, Aug 28 2015

CROSSREFS

Equals A250102(n)/16.

Sequence in context: A262405 A152841 A125083 * A262404 A299522 A300140

Adjacent sequences:  A094420 A094421 A094422 * A094424 A094425 A094426

KEYWORD

nonn

AUTHOR

Ralf Stephan, May 04 2004

STATUS

approved

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Last modified October 20 19:44 EDT 2018. Contains 316401 sequences. (Running on oeis4.)