Cubist
Senior Member
- Joined
- Oct 29, 2019
- Messages
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Brilliant! Thank you. I love the mapping of this problem to your string notation.I finally worked it out again...
Brilliant! Thank you. I love the mapping of this problem to your string notation.I finally worked it out again...
"_xx" <------- I think there ought to be an underscore before xxAny one-pair subset of the n-element set will end either in "_" (in which case there are Tn−1 ways to make the rest, which must include one pair); or in "_x" (Tn−2 ways); or in "xx" (Sn−3 ways, which must not include a pair). So
LHS ought to be Tn not SnSn=Tn−1+Tn−2+Sn−3
Correct on both counts. I've been too busy to check everything carefully.I spotted a couple of typos, and if @Dr.Peterson agrees then perhaps a moderator can correct these in post#20 (and then delete this post)
"_xx" <------- I think there ought to be an underscore before xx
LHS ought to be Tn not Sn
Tn=Tn−1+Tn−2+Sn−3
I'll have a goNow if you can work out a single recursion ... I haven't put any time into that.