1,4,14,46,146,...

[Michael Somos]

Dear Friends,

It is not generally recognized that sequences can often be run both
forward and backwards with recursion formulas. In the case of the
sequence in discussion, the natural extension in reverse is :

1394, 454, 146, 46, 14, 4, 1, 1/6, -1/36, -11/216, -49/1296, -179/7776, ...

As you can see, the last integer term is 1 and after that it becomes a
rational number with denominator 6^n. Given *any* sequence whatsoever,
it is *always* possible to arbitrarily set any term equal to whatever
you please. However, this will almost certainly break whatever pattern
or rule governs the sequence. If the sequence is patternless, then what
is the point in considering? There may be instances were a term or two
is altered for good reason. Note, there must be good reasons. Shalom,
Michael