|
%I #6 Mar 31 2012 12:36:08
%S 1,4,0,9,4,0,16,14,4,0,25,30,25,4,0,36,52,64,40,0,0,49,80,121,132,40,
%T 0,0,64,114,196,278,188,24,0,0,81,154,289,478,487,264,18,0,0,100,200,
%U 400,732,924,832,324,0,0,0,121,252,529,1040,1499,1810,1418,404,0,0,0,144,310,676
%N T(n,k)=Number of n-step S, NW and NE-moving king's tours on a kXk board summed over all starting positions
%C Table starts
%C .1.4..9..16...25....36....49....64.....81....100....121....144....169....196
%C .0.4.14..30...52....80...114...154....200....252....310....374....444....520
%C .0.4.25..64..121...196...289...400....529....676....841...1024...1225...1444
%C .0.4.40.132..278...478...732..1040...1402...1818...2288...2812...3390...4022
%C .0.0.40.188..487...924..1499..2212...3063...4052...5179...6444...7847...9388
%C .0.0.24.264..832..1810..3154..4864...6940...9382..12190..15364..18904..22810
%C .0.0.18.324.1418..3448..6581.10688..15769..21824..28853..36856..45833..55784
%C .0.0..0.404.2140..6380.13220.22996..35366..50330..67888..88040.110786.136126
%C .0.0..0.340.3060.10320.24892.46412..75567.111492.154187.203652.259887.322892
%C .0.0..0.280.3792.17052.44464.92628.159328.245946.350386.472648.612732.770638
%H R. H. Hardin, <a href="/A187377/b187377.txt">Table of n, a(n) for n = 1..287</a>
%F Empirical: T(1,k) = k^2
%F Empirical: T(2,k) = 3*k^2 - 5*k + 2
%F Empirical: T(3,k) = 9*k^2 - 24*k + 16 for k>1
%F Empirical: T(4,k) = 27*k^2 - 97*k + 88 for k>2
%F Empirical: T(5,k) = 69*k^2 - 322*k + 372 for k>3
%F Empirical: T(6,k) = 183*k^2 - 1035*k + 1432 for k>4
%F Empirical: T(7,k) = 487*k^2 - 3198*k + 5104 for k>5
%F Empirical: T(8,k) = 1297*k^2 - 9679*k + 17420 for k>6
%F Empirical: T(9,k) = 3385*k^2 - 28390*k + 56892 for k>7
%F Empirical: T(10,k) = 8911*k^2 - 82691*k + 181756 for k>8
%e Some n=4 solutions for 4X4
%e ..0..4..0..0....0..0..0..0....1..0..0..0....0..0..0..0....0..0..0..0
%e ..3..0..0..0....0..0..0..0....2..0..0..0....0..0..0..0....0..0..1..0
%e ..0..2..0..0....0..0..3..1....3..0..0..0....4..2..0..0....0..0..2..4
%e ..0..0..1..0....0..0..4..2....4..0..0..0....0..3..1..0....0..0..3..0
%Y Row 2 is A049451(n-1)
%Y Row 3 is A016790(n-2)
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Mar 09 2011
|
