bibkey: partridge2017a289832 authors: Hector J. Partridge year: 2017 title: “OEIS A289832, rectangles in rectangular lattice grids” doi: null url: https://oeis.org/A289832 claim: “In a lattice grid with three rows, the only oblique rectangles are squares of side length sqrt(2).” strata_touched:

• D5/S0/FiniteGeometry/RectangleIdentifiability/ThreeRowBlackoutMaximum license: “citation-only; OEIS source governed by https://oeis.org/LICENSE” triage: anchor

Rectangles in a three-row lattice strip

The COMMENTS line for column k=2 in OEIS A289832 states:

Column k=2 equals A140229 for n >= 3 as the only oblique rectangles are squares of side length sqrt(2), leading to the same formula.

The entry counts rectangles, including squares, on an (n+1) by (k+1) lattice grid. Thus k=2 is the three-row strip. These tilted squares are the unit diamonds with four corners on three consecutive columns. This geometric classification is known background for the blackout proof; it does not state presentation injectivity or the maximum blackout theorem. The formal result proves the required geometric classification locally, including its boundary cases, from integer perpendicularity and the parallelogram equations. No source counting formula is used as a premise.

Verified locator

• https://oeis.org/A289832

The complete original entry was read: official text at https://oeis.org/search?q=id:A289832&fmt=text, revision 28, March 11, 2018, 14:15:12; 3,062 bytes, SHA-256 c4d4ba65ec1637835606571093e605137b301eb0bf95fab3c06ed9d83705b859. The AUTHOR line credits Hector J. Partridge, July 13, 2017; the citation year is that contribution date, not the last revision date. The short quotation and bibliographic locator are retained without copying code.