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A193983 Number of ways to arrange 5 nonattacking triangular rooks on an n X n X n triangular grid. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

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.

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)

EXAMPLE

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

CROSSREFS

Column 5 of A193986.

Sequence in context: A244493 A221900 A229773 * A348701 A233234 A281694

Adjacent sequences: A193980 A193981 A193982 * A193984 A193985 A193986

KEYWORD

nonn

AUTHOR

R. H. Hardin Aug 10 2011

STATUS

approved

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Last modified February 8 15:16 EST 2023. Contains 360149 sequences. (Running on oeis4.)