The Online Encyclopedia of Integer Sequences (OEIS) is a reference catalogue of integer sequences maintained since 1964 by Neil Sloane and the OEIS Foundation. I have contributed to 26 sequences and authored seven of them. Most of my contributions fall into three themes: Latin squares (the subject of my PhD), enumeration of chess positions, and domination on the Cartesian product of cycles.
For the full list, see my “Richard Bean” author search on OEIS.
Sequences I authored
Latin squares and binary operations
- A080572
- Number of ordered pairs (i, j), 0 ≤ i, j < n, for which (i & j) is non-zero, where & is the bitwise AND operator.Added 22 Feb 2003.
- A090741
- Maximum number of transversals in a Latin square of order n.Added 3 Feb 2004.
- A092237
- Maximum number of intercalates in a Latin square of order n.Added 17 Feb 2004.
- A091323
- Minimum number of transversals in a Latin square of order 2n+1.Added 17 Feb 2004.
Domination numbers on products of cycles
- A094087
- Domination number of the Cartesian product of two n-cycles.Added 1 May 2004.
- A356649
- Domination number of the Cartesian product of three n-cycles.Added 19 Aug 2022.
- A356650
- Domination number of the Cartesian product of four n-cycles.Added 20 Aug 2022.
Sequences I extended
Chess-position enumeration
These sequences all fell out of the perft(10) calculation I ran in 2002–2003, which was the first public computation of the number of chess games at the end of ply 10.
- A048987
- Number of possible chess games at the end of ply n (i.e. perft(n)). I contributed perft(10) = 69,352,859,712,417.
- A079485
- Number of checkmate positions at ply n. I contributed the first published values at plies 7 and 8. The ply-6 term, 10,828, had stood since 1897.
- A007545
- Number of chess games with n plies (an alternative count).
- A083276
- Number of distinct chess positions after n plies, accounting for differences in castling rights and en-passant possibilities.
- A019319
- Number of possible chess diagrams after n plies.
Latin-square critical sets
- A063437
- Largest critical set in a Latin square of order n. My algorithms improved the 1982 bounds of Stinson and van Rees to lcs(5) = 11, lcs(7) ≥ 25, lcs(9) ≥ 45, and lcs(10) ≥ 57.
Source code for the Latin-square and chess programs that produced most of the above is in my source-code archive.