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

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

1,3

Comments

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.

Links

Table of n, a(n) for n=1..28.

Fletcher Collins, RookCount Program

Formula

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

Crossrefs

Possibly matches A011975 for all even n.

Cf. A001318.

Sequence in context: A364341 A335059 A047514 * A011975 A202112 A079249

Adjacent sequences: A345713 A345714 A345715 * A345717 A345718 A345719

Keyword

nonn,more

Author

Connor Mason Weisburg, Jun 24 2021

Status

approved