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A128561
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.
2
1, 3, 5, 21, 25, 539, 975, 847, 43095, 112651, 146523, 639331, 3663075, 69321747, 885243125, 19340767413, 25672050625, 381540593511, 189973174625, 12778871553, 886736325865, 1491476865543, 69915748770125, 305795988649809
OFFSET
1,2
FORMULA
For n >= 4, r(n) = -16*(n-1)*(n-2)/((2n-1)*(2n-5)*r(n-1)).
EXAMPLE
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))).
MAPLE
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, Oct 09 2007
CROSSREFS
Cf. A128560.
Sequence in context: A331395 A086175 A065926 * A032414 A062225 A288152
KEYWORD
frac,nonn
AUTHOR
Leroy Quet, Mar 10 2007
EXTENSIONS
More terms from R. J. Mathar, Oct 09 2007
STATUS
approved