<< Only if I were foolish enough to write them in terms of factorials. Why would I do that? >> Because e(11, 3) = e(9, 7) = 66 , perhaps? WFL On 5/27/14, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
On 27/05/2014 14:05, Fred Lunnon wrote:
Apologies --- I didn't read your previous post sufficiently carefully. So I must rephrase my critique: you stated << So, we're interested in the number of shortest paths - from (0,0) to A := (4N, 3), and - from (0,0) to B := (3N, 3N-2).
at which I might have more helpfully enquired why we should be interested in the first number at all?
Oh. Because I misread, obviously. (In a rather odd way.) OK, so actually it's (4N-1,3) and (3N,3N-2), and for the former the shortest paths are "obviously" those with N of NEE, N-1 of SEE, 1 of NNE, which does indeed give the same trinomial coefficient as for the latter.
[But imprecision over factorial arguments could possibly stiff your formulae with 0/0 instead.]
Only if I were foolish enough to write them in terms of factorials. Why would I do that?
-- g
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