cp's OEIS Frontend

A194498 T(n,k)=Number of ways to arrange k nonattacking queens on the lower triangle of an n X n board.

%I A194498 #10 Jul 22 2025 12:33:38
%S A194498 1,0,3,0,0,6,0,0,2,10,0,0,0,12,15,0,0,0,0,38,21,0,0,0,0,12,92,28,0,0,
%T A194498 0,0,0,82,188,36,0,0,0,0,0,8,330,344,45,0,0,0,0,0,0,118,1008,580,55,0,
%U A194498 0,0,0,0,0,4,802,2566,920,66,0,0,0,0,0,0,0,114,3708,5742,1390,78,0,0,0,0,0,0,0
%N A194498 T(n,k)=Number of ways to arrange k nonattacking queens on the lower triangle of an n X n board.
%C A194498 Table starts
%C A194498 ...1....0......0.......0........0........0........0........0........0......0..0
%C A194498 ...3....0......0.......0........0........0........0........0........0......0..0
%C A194498 ...6....2......0.......0........0........0........0........0........0......0..0
%C A194498 ..10...12......0.......0........0........0........0........0........0......0..0
%C A194498 ..15...38.....12.......0........0........0........0........0........0......0..0
%C A194498 ..21...92.....82.......8........0........0........0........0........0......0..0
%C A194498 ..28..188....330.....118........4........0........0........0........0......0..0
%C A194498 ..36..344...1008.....802......114........0........0........0........0......0..0
%C A194498 ..45..580...2566....3708.....1384.......64........0........0........0......0..0
%C A194498 ..55..920...5742...13280.....9890.....1644.......10........0........0......0..0
%C A194498 ..66.1390..11652...39734....50662....19306.....1210........0........0......0..0
%C A194498 ..78.2020..21926..104000...205512...146718....27198......484........0......0..0
%C A194498 ..91.2842..38802..244948...698688...820218...322782....26084.......38......0..0
%C A194498 .105.3892..65322..530632..2074530..3670288..2564988...531344....14870......0..0
%C A194498 .120.5208.105428.1072776..5525902.13846830.15372702..6285270...629414...3656..0
%C A194498 .136.6832.164214.2048056.13476246.45661556.74615814.51834064.11949712.501700.56
%H A194498 R. H. Hardin, <a href="/A194498/b194498.txt">Table of n, a(n) for n = 1..518</a>
%e A194498 Some solutions for n=6 k=4
%e A194498 ..0............0............0............0............0............0
%e A194498 ..0.0..........0.0..........0.1..........0.0..........1.0..........0.1
%e A194498 ..1.0.0........1.0.0........0.0.0........0.0.1........0.0.1........0.0.0
%e A194498 ..0.0.1.0......0.0.0.1......0.0.1.0......1.0.0.0......0.0.0.0......1.0.0.0
%e A194498 ..0.0.0.0.1....0.1.0.0.0....1.0.0.0.0....0.0.0.1.0....0.1.0.0.0....0.0.1.0.0
%e A194498 ..0.1.0.0.0.0..0.0.0.0.1.0..0.0.0.1.0.0..0.1.0.0.0.0..0.0.0.1.0.0..0.0.0.0.1.0
%Y A194498 Column 1 is A000217
%Y A194498 Column 2 is 2*A070893(n-2)
%K A194498 nonn,tabl
%O A194498 1,3
%A A194498 _R. H. Hardin_ Aug 26 2011