A193981 Number of ways to arrange 3 nonattacking triangular rooks on an nXnXn triangular grid.
0, 0, 0, 2, 23, 127, 468, 1352, 3310, 7190, 14260, 26330, 45885, 76237, 121688, 187712, 281148, 410412, 585720, 819330, 1125795, 1522235, 2028620, 2668072, 3467178, 4456322, 5670028, 7147322, 8932105, 11073545, 13626480, 16651840, 20217080
Offset: 1
Keywords
Examples
Some solutions for 5X5X5 ......0..........0..........0..........0..........0..........0..........0 .....0.0........0.0........0.0........0.0........0.1........0.0........0.1 ....0.0.1......1.0.0......0.1.0......0.1.0......0.0.0......0.1.0......1.0.0 ...0.1.0.0....0.0.0.1....1.0.0.0....0.0.0.1....1.0.0.0....1.0.0.0....0.0.0.0 ..1.0.0.0.0..0.1.0.0.0..0.0.1.0.0..0.0.1.0.0..0.0.1.0.0..0.0.0.0.1..0.0.0.1.0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..200
- 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) -14*a(n-2) +14*a(n-3) -14*a(n-5) +14*a(n-6) -6*a(n-7) +a(n-8)
Contribution from Vaclav Kotesovec, Aug 31 2012: (Start)
Empirical: G.f.: -x^4*(2 + 11*x + 17*x^2)/((-1+x)^7*(1+x))
Empirical: a(n) = 13*n/24 - 11*n^2/24 - 23*n^3/48 + 9*n^4/16 - 3*n^5/16 + n^6/48 + 1/4*floor(n/2)
(End)
Comments