A011975 -id:A011975 - cp's OEIS frontend

A011976 Covering numbers C(n,4,2).

1, 3, 3, 5, 6, 8, 9, 11, 12, 13, 18, 19, 20, 26, 27, 31, 35, 37, 39, 46, 48, 50, 59, 61, 63, 73, 75, 78, 88, 91, 94, 105, 108, 111, 124, 127, 130, 144, 147, 151, 165, 169, 173, 188, 192, 196, 213, 217, 221, 239, 243, 248, 266, 271, 276, 295, 300, 305, 326

Offset: 4

N. J. A. Sloane

Only differs from A240115 when n = 7, 9, 10, or 19. - Nathaniel Johnston, Jan 10 2024

CRC Handbook of Combinatorial Designs, 1996, p. 262.

D. Gordon, La Jolla Repository of Coverings
Index entries for covering numbers

Cf. A011975, A011977.

a(21)-a(62) from Nathaniel Johnston, Jan 10 2024

A345716 a(n) is the minimum number of nonattacking rooks required to attack every square on a size n right tetrahedral chessboard.

Original entry on oeis.org

1, 1, 3, 4, 6, 7, 11, 12, 17, 19, 24, 26, 33, 35, 42, 46, 53, 57, 66, 70, 79, 85, 94, 100, 111, 117, 129, 136

Offset: 1

Connor Mason Weisburg, Jun 24 2021

This sequence has been verified by brute force up to n = 27. It matches the covering numbers C(n+1, 3,2), A011975, for the first 14 terms, and it is conjectured that it matches for all even n. Link to the brute force program below. Computational runtime and increased complexity for minimum arrangements for bigger n account for the low number of terms. Other contributers: Fletcher Collins, Jennifer Gensler, Nick Jamesson, Chase Schwartzman, Evan Young, Dr. Nat Theim.

Fletcher Collins, RookCount Program

Possibly matches A011975 for all even n.

Cf. A001318.

For n == 0,2 (mod 6): a(n) = n*(n+1)/6 (conjectured).

cp's OEIS Frontend

A011976 Covering numbers C(n,4,2).

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