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Search: id:A128561
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| A128561 |
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a(n) = denominator of r(n): r(n) is such that the continued fraction (of rational terms) [r(1);r(2),...,r(n)] = n^2, for every positive integer n. |
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+0
2
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| 1, 3, 5, 21, 25, 539, 975, 847, 43095, 112651, 146523, 639331, 3663075, 69321747, 885243125, 19340767413, 25672050625, 381540593511, 189973174625, 12778871553, 886736325865, 1491476865543, 69915748770125, 305795988649809
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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For n >= 4, r(n) = -16*(n-1)*(n-2)/((2n-1)*(2n-5)*r(n-1)).
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EXAMPLE
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4^2 = 16 = 1 + 1/(1/3 +1/(-24/5 + 21/20)).
5^2 = 25 = 1 + 1/(1/3 +1/(-24/5 + 1/(20/21 -25/112))).
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MAPLE
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L2cfrac := proc(L, targ) local a, i; a := 1/(targ-op(1, L)) ; for i from 2 to nops(L) do a := 1/(a-op(i, L)) ; od: RETURN(a) ; end: A128561 := proc(nmax) local b, n, bnxt; b := [1] ; for n from 2 to nmax do bnxt := L2cfrac(b, n^2) ; b := [op(b), bnxt] ; od: [seq( denom(b[i]), i=1..nops(b))] ; end: A128561(30) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 09 2007
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CROSSREFS
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Cf. A128560.
Sequence in context: A103991 A086175 A065926 this_sequence A032414 A062225 A082699
Adjacent sequences: A128558 A128559 A128560 this_sequence A128562 A128563 A128564
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KEYWORD
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frac,nonn
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AUTHOR
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Leroy Quet Mar 10 2007
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 09 2007
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