Indeed, Brad, good idea! Please, submit! (and BTW, the Schlemmer was a delight to watch -- it was coproduced by (my) national TV (Belgium). Best, É. Catapulté de mon aPhone
Le 19 avr. 2020 à 19:36, Brad Klee <bradklee@gmail.com> a écrit :
Well, if contamination is a problem, then we would want to choose maximally spaced paths, regardless of time.
The simplest criteria is that two paths intersect only on the start and end points, then I count that:
2, 40, 350, 3528, 9240, 38808, 100352 . . .
On Sun, Apr 19, 2020 at 12:02 PM Éric Angelini <eric.angelini@skynet.be> wrote:
What about contamination, here: http://oeis.org/A333501 No clear sky in the graph, though!
à+ É. Catapulté de mon aPhone
Le 19 avr. 2020 à 19:02, Brad Klee <bradklee@gmail.com> a écrit :
https://oeis.org/A005260, see comment from April first 2019.
Now that it is dangerous for world-lines to intersect or to nearly intersect, should we also count tandem walks according to how well they will adhere to social distancing guidelines? for walks with minimum social distance 0,1,2, I get that:
a[n_, SocialDistance_] := 2 Total[ Times @@ #[[{1, -1}]] & /@ Partition[ Binomial[n, #]^2 & /@ Range[0, n], SocialDistance + 1, 1]]
Minimum social distance zero (A005260): a[#, 0]/2 & /@ Range[10] Out[] = {2, 18, 164, 1810, 21252, 263844, 3395016, 44916498, 607041380, 8345319268}
Minimum social distance one (nAn): a[#, 1] & /@ Range[10] Out[] = {2, 16, 198, 2368, 30100, 392544, 5248782, 71501056, 989177508, 13859716000}
Minimum social distance one (nAn): a[#, 2] & /@ Range[10] Out[] = {0, 2, 36, 656, 10400, 159750, 2402764, 35841344, 532676736, 7910428500}
See also: triadisches ballett, ha ha ha ha. https://youtu.be/mHQmnumnNgo?t=258 Obviously this was filmed before COVID...
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