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 A187606 T(n,k)=Number of n-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-bishop's tours (antidiagonal moves become knight moves) on a kXk board summed over all starting positions 7

%I #6 Mar 31 2012 12:36:08

%S 1,4,0,9,1,0,16,9,0,0,25,25,9,0,0,36,49,36,0,0,0,49,81,100,28,0,0,0,

%T 64,121,196,144,8,0,0,0,81,169,324,340,130,0,0,0,0,100,225,484,675,

%U 500,96,0,0,0,0,121,289,676,1120,1274,711,48,0,0,0,0,144,361,900,1675,2372,2083

%N T(n,k)=Number of n-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-bishop's tours (antidiagonal moves become knight moves) 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.....225

%C .0.1.9.25..49..81..121...169...225....289....361....441.....529.....625.....729

%C .0.0.9.36.100.196..324...484...676....900...1156...1444....1764....2116....2500

%C .0.0.0.28.144.340..675..1120..1675...2340...3115...4000....4995....6100....7315

%C .0.0.0..8.130.500.1274..2372..3953...5920...8273..11012...14137...17648...21545

%C .0.0.0..0..96.711.2083..4758..8979..14434..21526..29978...39790...50962...63494

%C .0.0.0..0..48.616.2936..8530.17611..32086..51955..76258..105978..140386..179482

%C .0.0.0..0...0.474.3780.12946.32869..68308.117760.187311..275272..379035..500919

%C .0.0.0..0...0.362.4168.19356.60155.132926.258163.445800..686062..997020.1370430

%C .0.0.0..0...0.124.3932.27316.92836.246888.539994.978245.1634722.2520047.3595001

%H R. H. Hardin, <a href="/A187606/b187606.txt">Table of n, a(n) for n = 1..287</a>

%F Empirical: T(1,k) = k^2

%F Empirical: T(2,k) = 4*k^2 - 12*k + 9 for k>1

%F Empirical: T(3,k) = 16*k^2 - 80*k + 100 for k>3

%F Empirical: T(4,k) = 55*k^2 - 380*k + 640 for k>5

%F Empirical: T(5,k) = 193*k^2 - 1700*k + 3620 for k>7

%F Empirical: T(6,k) = 680*k^2 - 7188*k + 18314 for k>9

%F Empirical: T(7,k) = 2344*k^2 - 28880*k + 85282 for k>11

%F Empirical: T(8,k) = 8156*k^2 - 114640*k + 385419 for k>13

%e Some n=5 solutions for 5X5

%e ..5..0..0..0..0....0..0..2..0..0....0..0..0..5..0....5..0..0..0..0

%e ..0..4..0..0..1....0..0..0..1..0....0..0..0..0..4....0..4..0..0..0

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

%e ..0..0..0..2..0....0..0..5..0..0....0..0..0..2..0....2..0..0..0..0

%e ..0..0..0..0..0....0..0..0..4..0....0..0..0..0..1....0..1..0..0..0

%Y Row 2 is A016754(n-2)

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ Mar 11 2011

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Last modified August 15 11:39 EDT 2024. Contains 375173 sequences. (Running on oeis4.)