cp's OEIS Frontend

A187286 T(n,k) = number of n-step one or two space at a time rook's tours on a k X k board summed over all starting positions.

%I A187286 #8 Oct 24 2023 18:00:39
%S A187286 1,4,0,9,8,0,16,36,8,0,25,80,108,8,0,36,140,328,288,0,0,49,216,672,
%T A187286 1256,720,0,0,64,308,1128,3084,4576,1440,0,0,81,416,1696,5712,13640,
%U A187286 15424,2304,0,0,100,540,2376,9120,28224,57288,47648,2664,0,0,121,680,3168
%N A187286 T(n,k) = number of n-step one or two space at a time rook's tours on a k X k board summed over all starting positions.
%C A187286 Table starts
%C A187286 .1.4....9.....16.......25.......36.......49.......64......81....100....121
%C A187286 .0.8...36.....80......140......216......308......416.....540....680....836
%C A187286 .0.8..108....328......672.....1128.....1696.....2376....3168...4072...5088
%C A187286 .0.8..288...1256.....3084.....5712.....9120....13288...18216..23904..30352
%C A187286 .0.0..720...4576....13640....28224....48232....73408..103692.139056.179500
%C A187286 .0.0.1440..15424....57288...134408...248208...397152..580328.797160
%C A187286 .0.0.2304..47648...228512...616752..1241936..2102944.3192912
%C A187286 .0.0.2664.134944...866888..2732016..6049424.10906120
%C A187286 .0.0.1512.345120..3123680.11693984.28716816
%C A187286 .0.0....0.789696.10664384.48391584
%H A187286 R. H. Hardin, <a href="/A187286/b187286.txt">Table of n, a(n) for n = 1..117</a>
%F A187286 Empirical: T(1,k) = k^2
%F A187286 Empirical: T(2,k) = 8*k^2 - 12*k for k>1
%F A187286 Empirical: T(3,k) = 56*k^2 - 160*k + 72 for k>3
%F A187286 Empirical: T(4,k) = 380*k^2 - 1532*k + 1224 for k>5
%F A187286 Empirical: T(5,k) = 2540*k^2 - 12896*k + 14016 for k>7
%F A187286 Empirical: T(6,k) = 16752*k^2 - 101420*k + 136160 for k>9
%F A187286 Empirical: T(7,k) = 109360*k^2 - 763776*k + 1206864 for k>11
%F A187286 Empirical: T(8,k) = 708492*k^2 - 5580668*k + 10074432 for k>13
%F A187286 Empirical: T(9,k) = 4562676*k^2 - 39873424*k + 80572112 for k>15
%F A187286 Empirical: T(10,k) = 29244672*k^2 - 280021012*k + 623972304 for k>17
%e A187286 Some n=4 solutions for 4X4
%e A187286 ..0..0..0..0....0..0..0..0....0..0..0..0....4..0..0..0....0..0..0..0
%e A187286 ..3..0..4..0....2..0..3..4....2..3..0..0....3..0..2..0....0..0..0..0
%e A187286 ..2..1..0..0....1..0..0..0....0..4..0..0....0..0..0..0....4..0..1..0
%e A187286 ..0..0..0..0....0..0..0..0....1..0..0..0....0..0..1..0....3..0..2..0
%K A187286 nonn,tabl
%O A187286 1,2
%A A187286 _R. H. Hardin_, Mar 08 2011