A187299 - OEIS

%I #11 Apr 23 2018 08:34:12

%S 0,0,54,196,480,876,1398,2036,2790,3660,4646,5748,6966,8300,9750,

%T 11316,12998,14796,16710,18740,20886,23148,25526,28020,30630,33356,

%U 36198,39156,42230,45420,48726,52148,55686,59340,63110,66996,70998,75116,79350,83700

%N Number of 4-step one space leftwards or up, two space rightwards or down asymmetric rook's tours on an n X n board summed over all starting positions.

%C Row 4 of A187296.

%H R. H. Hardin, <a href="/A187299/b187299.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 58*n^2 - 232*n + 180 for n>5.

%F Conjectures from _Colin Barker_, Apr 23 2018: (Start)

%F G.f.: 2*x^3*(27 + 17*x + 27*x^2 - 15*x^3 + 7*x^4 - 5*x^5) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.

%F (End)

%e Some solutions for 4 X 4:

%e ..1..0..0..0....0..0..0..0....0..0..1..0....0..0..0..0....0..0..0..0

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

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

%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..3..0..0....0..0..0..0

%Y Cf. A187296.

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 08 2011