A193982 Number of ways to arrange 4 nonattacking triangular rooks on an nXnXn triangular grid.
0, 0, 0, 0, 0, 18, 233, 1449, 6213, 20993, 59943, 150903, 344323, 726033, 1434678, 2685046, 4798206, 8240022, 13669026, 21995586, 34453386, 52685556, 78846471, 115721991, 166869131, 236778399, 331059729, 456655745, 622083189, 837706779
Offset: 1
Keywords
Examples
Some solutions for 6X6X6 .......0............0............0............0............0............0 ......0.0..........0.0..........1.0..........0.0..........0.1..........0.0 .....0.0.1........1.0.0........0.0.0........0.1.0........1.0.0........1.0.0 ....0.1.0.0......0.0.0.1......0.0.0.1......0.0.0.1......0.0.0.0......0.0.1.0 ...1.0.0.0.0....0.1.0.0.0....0.0.1.0.0....1.0.0.0.0....0.0.0.1.0....0.1.0.0.0 ..0.0.0.0.1.0..0.0.0.0.1.0..0.1.0.0.0.0..0.0.1.0.0.0..0.0.1.0.0.0..0.0.0.0.0.1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..89
- Christopher R. H. Hanusa, Thomas Zaslavsky, A q-queens problem. VII. Combinatorial types of nonattacking chess riders, arXiv:1906.08981 [math.CO], 2019.
Formula
Empirical: a(n) = 6*a(n-1) -12*a(n-2) +2*a(n-3) +27*a(n-4) -36*a(n-5) +36*a(n-7) -27*a(n-8) -2*a(n-9) +12*a(n-10) -6*a(n-11) +a(n-12)
Contribution from Vaclav Kotesovec, Aug 31 2012: (Start)
Empirical: G.f.: -x^6*(18 + 125*x + 267*x^2 + 279*x^3 + 151*x^4)/((-1+x)^9*(1+x)^3)
Empirical: a(n) = 87*n/40 - 57*n^2/32 - 253*n^3/96 + 1385*n^4/384 - 139*n^5/80 + 27*n^6/64 - 5*n^7/96 + n^8/384 + (3 - 11*n/8 + n^2/8)*floor(n/2)
(End)
Comments