Actually, ignoring the (-1)st term, these are A058797 and A058798. Regards, Max On Wed, Feb 26, 2014 at 11:57 AM, Max Alekseyev <maxale@gmail.com> wrote:
Hi Richard,
You miscalculated the 5th term, which should be 33/85 not 35/89. But still the sequences are not in the OEIS. Here is my PARI/GP one-liner for first 20 terms:
? apply(abs,contfracpnqn(vector(20,n,(-1)^(n-1)*n),20)) %1 = [1 1 1 2 7 33 191 1304 10241 90865 898409 9791634 116601199 1506023953 20967734143 313009988192 4987192076929 84469255319601 1515459403675889 28709259414522290 572669728886769911]
[0 1 2 5 18 85 492 3359 26380 234061 2314230 25222469 300355398 3879397705 54011212472 806288789375 12846609417528 217586071308601 3903702674137290 73952764737299909 1475151592071860890]
Regards, Max
On Wed, Feb 26, 2014 at 11:40 AM, rkg <rkg@cpsc.ucalgary.ca> wrote:
Sorry if this is well known to those who well know it, but the following seem not to be in OEIS:
1, 1, 2, 7, 35, 191, 1304, ... 1, 2, 5, 18, 89, 492, 3359, ...
Presumably because I've made a stupid mistake in my hand clculations.
They are the numerators and denominators of the convergents to the negative continued fraction 1 - 1/(2 - 1/(3 - 1/(4 - ...))) R.
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