While you and me, Éric, may think these sequences are something worthwhile, I am anticipating more of a clash with the editors: https://oeis.org/draft/A334237 (one complaint already!) Incidentally, I made a transcription error on the other sequence, so the non-intersecting walks are actually counted by: A267981: 2, 6, 40, 350, 3528, 9240, 38808, 100352 . . . but I haven't had time to work out the proof just yet. Anyways, who cares about the integers? The performance is sooo much more fun and interesting! I'm glad you liked the ballett video. The "Gelbe Marsch" involves some impressive footwork, but I'm not sure that is even my favorite part. In movement three, the "Schwarze Wirbeln" is also quite impressive from a maths viewpoint, and a great starting place for the conclusion: https://www.youtube.com/watch?v=Yfi6pfZ2XEo&feature=youtu.be&t=1110 What better way to practice social distancing than to start out completely alone and then spiral out of scene in to the dark surroundings? Pretty soon here I may have to do something similar myself. Cheers, Brad On Sun, Apr 19, 2020 at 12:58 PM Éric Angelini <eric.angelini@skynet.be> wrote:
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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