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a(n) is the minimum number of nonattacking rooks required to attack every square on a size n right tetrahedral chessboard.
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%I #16 Jul 13 2021 19:43:35

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

%T 111,117,129,136

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

%C 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.

%H Fletcher Collins, <a href="https://github.com/fletchc/rookount">RookCount Program</a>

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

%Y Possibly matches A011975 for all even n.

%Y Cf. A001318.

%K nonn,more

%O 1,3

%A _Connor Mason Weisburg_, Jun 24 2021