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... --Brad