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.

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

Links

Table of n, a(n) for n=1..24.

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

Adjacent sequences: A128558 A128559 A128560 * A128562 A128563 A128564

Keyword

frac,nonn

Author

Leroy Quet, Mar 10 2007

Extensions

More terms from R. J. Mathar, Oct 09 2007

Status

approved