A193986 T(n,k) is the number of ways to arrange k nonattacking triangular rooks on an nXnXn triangular grid.

1, 0, 3, 0, 0, 6, 0, 0, 3, 10, 0, 0, 0, 15, 15, 0, 0, 0, 2, 45, 21, 0, 0, 0, 0, 23, 105, 28, 0, 0, 0, 0, 0, 127, 210, 36, 0, 0, 0, 0, 0, 18, 468, 378, 45, 0, 0, 0, 0, 0, 0, 233, 1352, 630, 55, 0, 0, 0, 0, 0, 0, 6, 1449, 3310, 990, 66, 0, 0, 0, 0, 0, 0, 0, 270, 6213, 7190, 1485, 78, 0, 0, 0, 0

Offset: 1

Author

R. H. Hardin, Aug 10 2011

Keywords

• nonn
• tabl

Comments

Empirical: minimum-n nonzero T(n,k) is at n=k+floor(k/2) and this T(k+floor(k/2),k) is A002047((k-1)/2) for k odd

Table starts

...1....0......0.......0........0........0.........0.........0........0.......0

...3....0......0.......0........0........0.........0.........0........0.......0

...6....3......0.......0........0........0.........0.........0........0.......0

..10...15......2.......0........0........0.........0.........0........0.......0

..15...45.....23.......0........0........0.........0.........0........0.......0

..21..105....127......18........0........0.........0.........0........0.......0

..28..210....468.....233........6........0.........0.........0........0.......0

..36..378...1352....1449......270........0.........0.........0........0.......0

..45..630...3310....6213.....3195......166.........0.........0........0.......0

..55..990...7190...20993....21273.....4902........28.........0........0.......0

..66.1485..14260...59943...101484....54771......4842.........0........0.......0

..78.2145..26330..150903...386052...382439....104448......2532........0.......0

..91.3003..45885..344323..1243899..1976455...1127473....140598......244.......0

.105.4095..76237..726033..3527469..8250687...8147469...2568288...120052.......0

.120.5460.121688.1434678..9035376.29309540..44813100..27060693..4373740...49620

.136.7140.187712.2685046.21297492.91705972.201616740.200826477.71690568.5227020

Examples

			Some solutions for n=5 k=3
......0..........0..........0..........0..........1..........0..........0
.....0.0........0.0........0.0........0.1........0.0........0.0........0.1
....0.1.0......0.0.1......1.0.0......0.0.0......0.0.0......1.0.0......1.0.0
...0.0.0.1....1.0.0.0....0.0.1.0....0.0.1.0....0.1.0.0....0.0.1.0....0.0.1.0
..0.0.1.0.0..0.0.0.1.0..0.1.0.0.0..1.0.0.0.0..0.0.0.1.0..0.0.0.0.1..0.0.0.0.0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..551

Crossrefs

Row sums plus 1 give A289709.

Column 1 is A000217.

Column 2 is A050534.