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A187296 T(n,k)=Number of n-step one space leftwards or up, two space rightwards or down asymmetric rook's tours on a kXk board summed over all starting positions.

%I A187296 #8 Jul 22 2025 10:41:29
%S A187296 1,4,0,9,4,0,16,18,2,0,25,40,36,0,0,36,70,98,54,0,0,49,108,198,196,90,
%T A187296 0,0,64,154,330,480,416,144,0,0,81,208,494,876,1208,884,108,0,0,100,
%U A187296 270,690,1398,2400,3006,1368,72,0,0,121,340,918,2036,4092,6520,6264,2028,54
%N A187296 T(n,k)=Number of n-step one space leftwards or up, two space rightwards or down asymmetric rook's tours on a kXk board summed over all starting positions.
%C A187296 Table starts
%C A187296 .1.4...9...16....25.....36.....49......64......81.....100.....121.....144
%C A187296 .0.4..18...40....70....108....154.....208.....270.....340.....418.....504
%C A187296 .0.2..36...98...198....330....494.....690.....918....1178....1470....1794
%C A187296 .0.0..54..196...480....876...1398....2036....2790....3660....4646....5748
%C A187296 .0.0..90..416..1208...2400...4092....6208....8766...11752...15166...19008
%C A187296 .0.0.144..884..3006...6520..11896...18832...27478...37696...49508...62896
%C A187296 .0.0.108.1368..6264..15596..31172...52256...79634..112568..151266..195512
%C A187296 .0.0..72.2028.12778..37124..81362..145100..231552..338044..465734..613212
%C A187296 .0.0..54.2968.25716..87432.209700..399524..668522.1010572.1430378.1921532
%C A187296 .0.0...0.3096.44824.187924.505878.1044900.1847506.2912204.4254568
%H A187296 R. H. Hardin, <a href="/A187296/b187296.txt">Table of n, a(n) for n = 1..201</a>
%F A187296 Empirical: T(1,k) = k^2
%F A187296 Empirical: T(2,k) = 4*k^2 - 6*k for k>1
%F A187296 Empirical: T(3,k) = 16*k^2 - 44*k + 18 for k>3
%F A187296 Empirical: T(4,k) = 58*k^2 - 232*k + 180 for k>5
%F A187296 Empirical: T(5,k) = 214*k^2 - 1080*k + 1152 for k>7
%F A187296 Empirical: T(6,k) = 788*k^2 - 4736*k + 6256 for k>9
%F A187296 Empirical: T(7,k) = 2776*k^2 - 19580*k + 30728 for k>11
%F A187296 Empirical: T(8,k) = 9878*k^2 - 79388*k + 143388 for k>13
%F A187296 Empirical: T(9,k) = 35254*k^2 - 316744*k + 644876 for k>15
%F A187296 Empirical: T(10,k) = 124248*k^2 - 1238146*k + 2807812 for k>17
%e A187296 Some n=4 solutions for 4X4
%e A187296 ..0..0..0..0....0..0..0..0....4..3..2..0....0..0..0..4....0..1..0..0
%e A187296 ..0..0..0..1....3..2..4..0....0..0..1..0....0..2..0..3....0..3..0..4
%e A187296 ..0..0..4..3....0..1..0..0....0..0..0..0....0..1..0..0....0..2..0..0
%e A187296 ..0..0..0..2....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%K A187296 nonn,tabl
%O A187296 1,2
%A A187296 _R. H. Hardin_ Mar 08 2011