bibkey: kurkov2025a392095 authors: Mikhail Kurkov year: 2025 title: “OEIS A392095, antidiagonal array and the shifted A088713 column” doi: null url: https://oeis.org/A392095 claim: “Conjecture: A(n,0) = A088713(n+1).” strata_touched:

• D5/S1/Recurrence/Algebraic/AntidiagonalArraySourceSeries license: CC-BY-SA-4.0 triage: anchor

Kurkov’s antidiagonal array

Mikhail Kurkov’s entry is dated December 30, 2025. Its NAME and FORMULA in the fixed official export read:

Array read by downward antidiagonals: A(n,k) = A(n-1,k+1) + Sum_{j=0..k} A(n-1,j)*A(k-j,0) with A(0,k) = 1.

Conjecture: A(n,0) = A088713(n+1).

The offset is 0,3. The recurrence applies for positive n and every natural k; replacing n by n+1 gives the Lean predicate IsArray. The sum includes j=0 and j=k. The conjecture includes n=0, where the column value is one and the source coefficient is that at index one. The independent source equation is quoted in hanna2003a088713.md. Neither the example array nor the PARI program is an additional premise.

Verified locator

• URL: https://oeis.org/A392095
• Immutable export: https://github.com/oeis/oeisdata/blob/892a05dd4941ae76caee5906ea33ceedf3389b1d/seq/A392/A392095.seq
• Revision line: %I A392095 #4 Jan 04 2026 21:07:20.
• Author line: %A A392095 _Mikhail Kurkov_, Dec 30 2025.
• License: OEIS Foundation, Creative Commons Attribution-ShareAlike 4.0, https://oeis.org/wiki/The_OEIS_End-User_License_Agreement and https://creativecommons.org/licenses/by-sa/4.0/.

The immutable export was read directly on September 21, 2026 (Singapore). This reading establishes the fixed quotations, not the current live entry. No earlier complete resolution was found in the bounded repository and Lean-library searches described in the corresponding Problems dossier; this is not a worldwide priority claim.