OEIS Contributions
Why these. These sequences have nothing in common at the level of subject. They range over Ramsey theory, extremal graph theory, knot theory, and the algebra of graphs. What they share is how they were found. Each is a quantity with no known formula, computed exactly by SAT solving or exhaustive search, pushed one value past the published frontier, and checked against all prior art before it was submitted. The spread across fields is deliberate: it is evidence that the method travels. And the method has a direction. The computed values are where I go looking for structure. The Rado numbers began as a column of computed integers and ended as a proved theorem; the rest are trailheads, some already climbed, others marked for whoever arrives next. The OEIS is where the results live, as permanent reference points anyone can build on or check.
Author search: oeis.org/search?q=alex+towell.
Authored sequences
These sequences were created and first populated by me.
| Sequence | Description | Domain |
|---|---|---|
| A394445 | Distinct-variable 2-color Rado numbers for x+y=nz: the least k such that every 2-coloring of {1,…,k} has a monochromatic distinct-variable solution | Ramsey theory |
| A394661 | Triangle T(n,k): number of prime knots with n crossings and three-genus k | Knot theory |
| A395521 | Number of non-isomorphic abelian groups appearing as the sandpile group K(G) over graphs on n vertices | Algebraic graph theory |
| A395644 | Number of fibered prime knots with n crossings | Knot theory |
A394445 is backed by a closed-form theorem (a proof that the distinct 2-color Rado number for x+y=kz follows an explicit parity-dependent formula for all k >= 8), with a 500-term b-file. A394661 and A395644 come from a census of the KnotInfo prime-knot tables; A395521 from an exhaustive sandpile-group computation.
Extended sequences
Classical Zarankiewicz-problem sequences (originally by N. J. A. Sloane) where I computed and added new terms past the known frontier.
| Sequence | Description | My terms |
|---|---|---|
| A006615 | z(n,n;3,4): least k forcing an all-ones 3x4 submatrix in an n x n 0/1 matrix | a(10)=67; a(11)=79 (in review) |
| A006622 | z(n,n+1;3,4): same for n x (n+1) matrices | a(9)=61; a(10)=73 (in review) |
| A006625 | z(n,n+2;3,4): same for n x (n+2) matrices | a(9)=67; a(10)=79 (in review) |
The Zarankiewicz extensions use SAT: a satisfying assignment exhibits a dense matrix (a lower bound), and an unsatisfiable instance proves the matching upper bound. The most recent terms required a double-lex symmetry-breaking encoding to make the upper-bound proof tractable: the plain encoding could not settle z(10,11;3,4) in seven days, while the symmetry-broken version proved it in 27 minutes.
In review (June 2026)
- A006615 a(11)=79, A006622 a(10)=73, A006625 a(10)=79 (the three exact Zarankiewicz values above), proposed June 5 2026.
The A394445 b-file (500 terms) is already approved and live.
Reviewers
These submissions were reviewed and approved by OEIS editors including Michel Marcus, Sean A. Irvine, Max Alekseyev, and Jon E. Schoenfield.
The OEIS has been a shared ledger of integer sequences since 1964. Adding a term is a small, permanent contribution to a commons that outlasts any one project: a number that was unknown is now known, checked, and citable by anyone who needs it.