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

1,6

Comments

Column 4 of A193986

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)

Example

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

Crossrefs

Sequence in context: A016312 A017916 A016307 * A021094 A275963 A125453

Adjacent sequences: A193979 A193980 A193981 * A193983 A193984 A193985

Keyword

nonn

Author

R. H. Hardin Aug 10 2011

Status

approved