bibkey: udovenko2026a395531 authors: Aleksei Udovenko year: 2026 title: “OEIS A395531, greedy-brick row births” doi: null url: https://oeis.org/A395531/internal claim: “Conjecture: when n = a(m) for some m, we have a(n) = n(n+3)/2 - m. Verified experimentally up to m=1172, n=688491.” strata_touched:

• D5/S3/Combinatorics/GreedyBrick/OriginalIdentity license: citation-only triage: anchor

Greedy-brick row births

OEIS A395531, revision 30, attributes the quoted conjecture to Aleksei Udovenko, May 7, 2026. Bricks have integer widths 1,2,3,… and unit height. Each brick is placed as close to the vertical axis as possible on the highest fully supported row. The sequence records the width of the first brick in each row, numbered from one.

The entry’s Python generator stores rows from bottom to top. It creates a new top row if the current width fits on the old top row; otherwise it extends the highest row on which the whole brick fits. The independently defined sourceRowStep stores these same rows in the reverse order. The frozen row-transition and labelled-history results supply the capacity and physical placement correspondence. No generator source is redistributed.

Verified locator

• Original assertion and generator: https://oeis.org/A395531/internal
• Related placement sequence: https://oeis.org/A233380