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Cyborg Mathematics

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Mathematical chemistry

A benzenoid is a molecule whose carbon atoms form fused hexagonal rings, and counting the possible shapes by size is an old problem in mathematical chemistry. I reproduced a peer-reviewed census in full, found six errors in it (in its tables, a figure caption and the text), and extended its breakdown tables two sizes further.

2 results

Results

Numbered by their place in the strongest-first list

  1. 06

    A peer-reviewed census of benzenoid molecules reproduced in full, with errors found and its tables extended

    I reproduced every table of a peer-reviewed 2018 census of benzenoid molecules, shapes made of fused hexagonal rings of carbon. I found ▲ errors (in its tables, a figure caption and the text), each with a corrected value, while everything else matched exactly. I sent them to the authors, who have not yet confirmed them. I then extended the census’s breakdown tables two sizes further, to ▲ molecules at the largest size. The OEIS already had the totals at both new sizes, and mine agree with them.

    Checked outside this site

    • MatchThe totals at the two new sizes match the counts already in the OEIS. OEIS A018190
    • CreditThe errors and corrected values went to the census authors, who have not yet confirmed them,
    • ArchiveData and code archived, . Zenodo DOI
    ShapesChemistry
  2. 12

    A fullerene table in the OEIS that an old bug fix never reached, corrected

    Fullerenes are cage molecules made of carbon, like the buckyball. The OEIS table that counts them by size took its larger values from a 2006 data file made before a bug in the counting program was fixed, so those values were too small. I replaced ▲ of them, of which had been wrong for about ▲ years.

    Checked outside this site

    • OEIS editorMichael De Vlieger published the fix and Andrei Zabolotskii reviewed it, . OEIS A057210
    SequencesChemistry

Articles

There is no separate write-up for this field on the site yet; the results above link to their records.

Notes on the numbers marked ▲

  • Errors found in the published census paper while reproducing it (in its tables, a figure caption and the text), each with a corrected value: 6. I sent the errors and corrected values to the paper’s authors on August 17 and 27, 2026. They have not replied about them yet, and the corrections are not yet in a public document.
  • Benzenoid structures with 15 hexagons, two sizes past the published census (the total matches OEIS A018190): 74,207,910. The OEIS (A018190) already listed the total at this size, and my count matches it. What is new is the census’s breakdown of that total, which has not been peer reviewed yet.
  • Values of the OEIS fullerene table A057210, a(68) to a(100), replaced because its 2006 data file predated a program bug fix: 33. Of the values replaced, the ones at n = 69, 70, 71, 74 and 80 were already right.
  • Years, roughly, that the wrong values in A057210 stood (the data file dates from 2006): 20. An approximate span, from the 2006 data file to the August 2026 correction.