A187193 - OEIS

%I #15 Apr 19 2022 05:17:07

%S 0,0,1440,40896,364800,1902240,7197120,21960960,57407616,133531200,

%T 283488480,559247040,1038660480

%N Number of 6-turn rook's tours on an n X n board summed over all starting positions.

%F Empirical: a(n) = 32*n^7 - 258*n^6 + 846*n^5 - 1426*n^4 + 1234*n^3 - 428*n^2.

%F Empirical G.f.: 96*x^3*(15+306*x+812*x^2+503*x^3+44*x^4)/(1-x)^8. [_Colin Barker_, Jan 22 2012]

%e Some solutions for 3X3

%e ..0..0..1....0..0..6....3..2..1....0..0..1....0..4..5....0..0..3....0..3..2

%e ..3..4..2....0..4..5....0..0..0....4..6..5....1..0..0....0..5..4....6..0..0

%e ..0..5..6....2..3..1....4..5..6....3..0..2....2..3..6....1..6..2....5..4..1

%Y Row 6 of A187189.

%K nonn,more

%O 1,3

%A _R. H. Hardin_, Mar 06 2011