A187287 - OEIS

%I #21 Oct 24 2023 18:01:11

%S 0,8,36,80,140,216,308,416,540,680,836,1008,1196,1400,1620,1856,2108,

%T 2376,2660,2960,3276,3608,3956,4320,4700,5096,5508,5936,6380,6840,

%U 7316,7808,8316,8840,9380,9936,10508,11096,11700,12320,12956,13608,14276,14960,15660

%N Number of 2-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

%H R. H. Hardin, <a href="/A187287/b187287.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 8*n^2 - 12*n for n>1.

%F Empirical g.f.: 4*x^2*(2+3*x-x^2)/(1-x)^3. - _Colin Barker_, Jan 22 2012

%e Some solutions for 4 X 4:

%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..2..0..1

%e ..1..0..0..0....0..1..0..0....0..1..2..0....2..0..0..0....0..0..0..0

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

%e ..2..0..0..0....0..2..0..0....0..0..0..0....1..0..0..0....0..0..0..0

%p A187287:=n->`if`(n=1, 0, 8*n^2 - 12*n); seq(A187287(n), n=1..50); # _Wesley Ivan Hurt_, Feb 28 2014

%Y Row 2 of A187286.

%Y Cf. A014107.

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 08 2011