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A193986
T(n,k) is the number of ways to arrange k nonattacking triangular rooks on an nXnXn triangular grid.
8
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Aug 10 2011
STATUS
approved