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

1,3

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

Links

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

Example

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

Crossrefs

Row sums plus 1 give A289709.

Column 1 is A000217.

Column 2 is A050534.

Sequence in context: A330735 A127773 A194498 * A376203 A062688 A067181

Adjacent sequences: A193983 A193984 A193985 * A193987 A193988 A193989

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 10 2011

Status

approved