bibkey: barker2018a181278
authors: Colin Barker
year: 2018
title: "OEIS A181278, binary matrices with ordered rows and decreasing mod-2 Gram rows"
doi: null
url: https://oeis.org/A181278
claim: "a(n) = 4*a(n-1) + 4*a(n-2) - 16*a(n-3) for n>3."
strata_touched:
  - D5/S1/Words/Patterns/BarkerBinaryGramRecurrenceRefutation
license: citation-only
triage: anchor

OEIS A181278

The NAME line defines A181278 as follows:

Number of 2 X n binary matrices M with rows in strictly increasing order and rows of M*Mtranspose (mod 2) in strictly decreasing order.

The target FORMULA line, signed by Colin Barker on March 27, 2018, is:

a(n) = 4a(n-1) + 4a(n-2) - 16*a(n-3) for n>3.

The entry has offset 1, so the stated range includes n = 4 and reaches the published term a(1) = 0. The entry currently cites no proof or refutation of this recurrence. Its links contain only the sequence b-file, and its reference section is empty. The OEIS conjecture scan reported no settlement marker.

Verified locator

• URL: https://oeis.org/A181278
• NAME (verbatim): Number of 2 X n binary matrices M with rows in strictly increasing order and rows of M*Mtranspose (mod 2) in strictly decreasing order.
• FORMULA conjecture line (verbatim): a(n) = 4a(n-1) + 4a(n-2) - 16*a(n-3) for n>3.
• Attribution, from the preceding FORMULA line (verbatim): Conjectures from Colin Barker, Mar 27 2018: (Start)