cp's OEIS Frontend

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

%I A193986 #12 Sep 12 2019 19:28:20
%S A193986 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,
%T A193986 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,
%U A193986 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
%N A193986 T(n,k) is the number of ways to arrange k nonattacking triangular rooks on an nXnXn triangular grid.
%C A193986 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
%C A193986 Table starts
%C A193986 ...1....0......0.......0........0........0.........0.........0........0.......0
%C A193986 ...3....0......0.......0........0........0.........0.........0........0.......0
%C A193986 ...6....3......0.......0........0........0.........0.........0........0.......0
%C A193986 ..10...15......2.......0........0........0.........0.........0........0.......0
%C A193986 ..15...45.....23.......0........0........0.........0.........0........0.......0
%C A193986 ..21..105....127......18........0........0.........0.........0........0.......0
%C A193986 ..28..210....468.....233........6........0.........0.........0........0.......0
%C A193986 ..36..378...1352....1449......270........0.........0.........0........0.......0
%C A193986 ..45..630...3310....6213.....3195......166.........0.........0........0.......0
%C A193986 ..55..990...7190...20993....21273.....4902........28.........0........0.......0
%C A193986 ..66.1485..14260...59943...101484....54771......4842.........0........0.......0
%C A193986 ..78.2145..26330..150903...386052...382439....104448......2532........0.......0
%C A193986 ..91.3003..45885..344323..1243899..1976455...1127473....140598......244.......0
%C A193986 .105.4095..76237..726033..3527469..8250687...8147469...2568288...120052.......0
%C A193986 .120.5460.121688.1434678..9035376.29309540..44813100..27060693..4373740...49620
%C A193986 .136.7140.187712.2685046.21297492.91705972.201616740.200826477.71690568.5227020
%H A193986 R. H. Hardin, <a href="/A193986/b193986.txt">Table of n, a(n) for n = 1..551</a>
%e A193986 Some solutions for n=5 k=3
%e A193986 ......0..........0..........0..........0..........1..........0..........0
%e A193986 .....0.0........0.0........0.0........0.1........0.0........0.0........0.1
%e A193986 ....0.1.0......0.0.1......1.0.0......0.0.0......0.0.0......1.0.0......1.0.0
%e A193986 ...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
%e A193986 ..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
%Y A193986 Row sums plus 1 give A289709.
%Y A193986 Column 1 is A000217.
%Y A193986 Column 2 is A050534.
%K A193986 nonn,tabl
%O A193986 1,3
%A A193986 _R. H. Hardin_, Aug 10 2011