Number of ways to arrange 6 nonattacking knights on the lower triangle of an nXn n X n board

_R. H. Hardin (rhhardin(AT)att.net) _ Aug 26 2011

editing

approved

R. H. Hardin, <a href="/A194490/b194490.txt">Table of n, a(n) for n = 1..42</a>

allocated for Ron HardinNumber of ways to arrange 6 nonattacking knights on the lower triangle of an nXn board

0, 0, 0, 1, 230, 4257, 44005, 312296, 1693828, 7449231, 27785786, 90732814, 265594944, 709634275, 1755164932, 4063548824, 8885486966, 18484419808, 36802865115, 70481362597, 130377759323, 233782433461, 407584477894

1,5

Column 6 of A194492

Empirical: a(n) = (1/46080)*n^12 + (1/7680)*n^11 - (17/3072)*n^10 - (13/4608)*n^9 + (6635/9216)*n^8 - (66667/23040)*n^7 - (2096789/46080)*n^6 + (1744105/4608)*n^5 + (10251671/11520)*n^4 - (107575289/5760)*n^3 + (46056797/1440)*n^2 + (984185/3)*n - 1221248 for n>13

Some solutions for 5X5

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

..0.0........0.0........1.0........0.0........1.1........0.0........0.1

..1.0.0......1.0.0......0.0.0......1.0.1......1.0.0......1.0.0......0.0.0

..0.0.0.1....1.0.0.1....1.0.0.0....0.0.0.1....0.0.0.1....0.0.0.1....0.0.0.1

..1.0.1.0.1..0.0.0.1.1..1.1.0.1.0..1.0.1.0.1..0.0.1.0.1..1.0.1.1.1..1.0.1.1.0

allocated

nonn

R. H. Hardin (rhhardin(AT)att.net) Aug 26 2011

approved

editing

allocated for Ron Hardin

allocated

approved