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A097572
Numerator of f(n) where f(1) = 1, f(n+1) = n^2/f(n) + f(n)/n^2 + 2.
0
1, 4, 4, 169, 555025, 14291007025, 8480906296345283491681, 3964171123687651228091479334301620432503354561, 1124604806436444518574523753367158577376786150279857801748598100182341756509785760684694337921
OFFSET
1,2
LINKS
Y. Chen and others, Variation of a Ukrainian Olympiad Problem: Problem 10982, Amer. Math. Monthly, 111 (No. 7, 2004), 631-632.
FORMULA
f(n) -> n + 1/2.
EXAMPLE
1, 4, 4, 169/36, 555025/97344, 14291007025/2161134144, ...
MATHEMATICA
nxt[{n_, a_}]:={n+1, n^2/a+a/n^2+2}; NestList[nxt, {1, 1}, 10][[All, 2]]//Numerator (* Harvey P. Dale, Sep 22 2020 *)
CROSSREFS
Cf. A097573.
Sequence in context: A055071 A213142 A357540 * A160365 A264517 A080509
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Aug 29 2004
STATUS
approved