A110216
Total number of coverings of a cubic board with the minimal number of knights.
Original entry on oeis.org
1, 1, 12, 156, 888
Offset: 1
Nikolaus Meyberg (Nikolaus.Meyberg(AT)t-online.de), Jul 17 2005
a(3) = 12, since reflections or rotations of
OOO KKK OOO
OKO OKO OKO
OOO OOO OOO generate twelve different coverings.
This sequence is a 3-dimensional analog of
A103315. a(n) =
A110219(n, n, n).
A102215 gives the number of inequivalent solutions.
A110217
Cone C(n,m,k) read by planes and rows, for 1 <= k <= m <= n: minimal number of knights needed to cover a k X m X n board.
Original entry on oeis.org
1, 2, 4, 8, 3, 4, 8, 4, 6, 6, 4, 4, 8, 4, 6, 6, 4, 6, 7, 8, 5, 4, 8, 4, 6, 6, 4, 6, 7, 8, 5, 6, 8, 10, 13, 6, 4, 6, 4, 7, 6, 4, 8, 8, 12, 6, 8, 10, 12
Offset: 1
Nikolaus Meyberg (Nikolaus.Meyberg(AT)t-online.de), Jul 17 2005
Cone starts:
1..2....3......4........5............6.................
...4.8..4.8....4.8......4.8..........4..6
........4.6.6..4.6.6....4.6.6........4..7..6
...............4.6.7.8..4.6.7..8.....4..8..8.12
........................5.6.8.10.13..6..8.10.12.?
.....................................8.11.12..?....
C(n, n, 1) =
A006075(n), C(n, k, 1) =
A098604(n, k), C(n, n, n) =
A110214(n).
A110218 gives number of inequivalent ways to cover the board using C(n, m, k) knights,
A110219 gives total number.
A110218
Cone C(n,m,k) read by planes and rows, for 1 <= k <= m <= n: Number of inequivalent coverings of a k X m X n board using A110217(n,m,k) knights.
Original entry on oeis.org
1, 1, 1, 1, 1, 2, 6, 2, 3, 1, 1, 7, 103, 6, 10, 3, 3, 2, 1, 8, 1, 2, 196, 2, 5, 2, 2, 1, 1, 3, 8, 1, 2, 8, 37, 1, 1, 451, 1, 33, 1, 1, 55, 1, 220, 16, 3, 12, 5
Offset: 1
Nikolaus Meyberg (Nikolaus.Meyberg(AT)t-online.de), Jul 17 2005
Cone starts:
1..1.....1........1.............1..................1........................
...1,.1..2,.6.....7,.103........2,.196.............1,.451
.........2,.3,.1..6,..10,.3.....2,...5,.2..........1,..33,..1
..................3,...2,.1,.8..2,...1,.1,.3.......1,..55,..1,.220
................................8,...1,.2,.8,.37..16,...3,.12,...5,.?
..................................................23,...2,..4,...?,....
Showing 1-3 of 3 results.