A193983 - OEIS

%I #17 Aug 19 2019 16:49:34

%S 0,0,0,0,0,0,6,270,3195,21273,101484,386052,1243899,3527469,9035376,

%T 21297492,46838142,97131762,191517192,361427508,656353494,1152094086,

%U 1961910990,3251400894,5257953789,8315944731,12888836064,19609755396

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

%H R. H. Hardin, <a href="/A193983/b193983.txt">Table of n, a(n) for n = 1..52</a>

%H Christopher R. H. Hanusa, Thomas Zaslavsky, <a href="https://arxiv.org/abs/1906.08981">A q-queens problem. VII. Combinatorial types of nonattacking chess riders</a>, arXiv:1906.08981 [math.CO], 2019.

%F 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).

%F Contribution from _Vaclav Kotesovec_, Aug 31 2012: (Start)

%F 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)).

%F 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).

%F (End)

%e Some solutions for 7 X 7 X 7

%e ........0..............0..............0..............0..............0

%e .......0.0............0.0............0.0............0.0............0.0

%e ......0.1.0..........0.1.0..........0.0.1..........1.0.0..........0.0.1

%e .....1.0.0.0........0.0.0.1........1.0.0.0........0.0.0.1........0.1.0.0

%e ....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

%e ...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

%e ..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

%Y Column 5 of A193986.

%K nonn

%O 1,7

%A _R. H. Hardin_ Aug 10 2011