A193983 Number of ways to arrange 5 nonattacking triangular rooks on an n X n X n triangular grid.

0, 0, 0, 0, 0, 0, 6, 270, 3195, 21273, 101484, 386052, 1243899, 3527469, 9035376, 21297492, 46838142, 97131762, 191517192, 361427508, 656353494, 1152094086, 1961910990, 3251400894, 5257953789, 8315944731, 12888836064, 19609755396

Offset: 1

Author

R. H. Hardin Aug 10 2011

Keywords

• nonn

Examples

			Some solutions for 7 X 7 X 7
........0..............0..............0..............0..............0
.......0.0............0.0............0.0............0.0............0.0
......0.1.0..........0.1.0..........0.0.1..........1.0.0..........0.0.1
.....1.0.0.0........0.0.0.1........1.0.0.0........0.0.0.1........0.1.0.0
....0.0.0.0.1......1.0.0.0.0......0.0.0.1.0......0.1.0.0.0......1.0.0.0.0
...0.0.0.1.0.0....0.0.1.0.0.0....0.1.0.0.0.0....0.0.0.0.1.0....0.0.0.0.1.0
..0.0.1.0.0.0.0..0.0.0.0.1.0.0..0.0.0.0.1.0.0..0.0.1.0.0.0.0..0.0.0.1.0.0.0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..52
• Christopher R. H. Hanusa, Thomas Zaslavsky, A q-queens problem. VII. Combinatorial types of nonattacking chess riders, arXiv:1906.08981 [math.CO], 2019.

Crossrefs

Column 5 of A193986.

Formula

Empirical: a(n) = 5*a(n-1) -5*a(n-2) -14*a(n-3) +30*a(n-4) +6*a(n-5) -50*a(n-6) +10*a(n-7) +44*a(n-8) -44*a(n-10) -10*a(n-11) +50*a(n-12) -6*a(n-13) -30*a(n-14) +14*a(n-15) +5*a(n-16) -5*a(n-17) +a(n-18).

Contribution from Vaclav Kotesovec, Aug 31 2012: (Start)

Empirical: G.f.: -3*x^7*(2 + 80*x + 625*x^2 + 2244*x^3 + 4898*x^4 + 7197*x^5 + 7237*x^6 + 5030*x^7 + 2294*x^8 + 633*x^9)/((-1+x)^11*(1+x)^5*(1+x+x^2)).

Empirical: a(n) = 3461*n/320 - 469*n^2/240 - 469*n^3/15 + 2383*n^4/64 - 76607*n^5/3840 + 23693*n^6/3840 - 2263*n^7/1920 + 53*n^8/384 - 7*n^9/768 + n^10/3840 + 4/3*floor(n/3) + (1359/32 - 247*n/8 + 245*n^2/32 - 13*n^3/16 + n^4/32)*floor(n/2) - 4/3*floor((1 + n)/3).

(End)