A251137 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no 2X2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements

40, 133, 133, 369, 416, 369, 919, 1002, 1002, 919, 2129, 2264, 1997, 2264, 2129, 4699, 4786, 4110, 4110, 4786, 4699, 10033, 9786, 8050, 8008, 8050, 9786, 10033, 20947, 19548, 15830, 14753, 14753, 15830, 19548, 20947, 43077, 38674, 30770, 27738, 25597

Offset

1,1

Comments

Table starts

....40....133....369....919...2129...4699...10033...20947...43077...87703

...133....416...1002...2264...4786...9786...19548...38674...76196..150192

...369...1002...1997...4110...8050..15830...30770...60088..117492..230956

...919...2264...4110...8008..14753..27738...51679...97758..186223..359276

..2129...4786...8050..14753..25597..46023...82431..151567..282371..536601

..4699...9786..15830..27738..46023..79226..135959..240780..434193..804400

.10033..19548..30770..51679..82431.135959..223663..380641..662361.1191797

.20947..38674..60088..97758.151567.240780..380641..620524.1035365.1793398

.43077..76196.117492.186223.282371.434193..662361.1035365.1653313.2742539

.87703.150192.230956.359276.536601.804400.1191797.1793398.2742539.4340190

Links

R. H. Hardin, Table of n, a(n) for n = 1..543

Formula

Empirical for column k:

k=1: a(n) = 5*a(n-1) -8*a(n-2) +2*a(n-3) +7*a(n-4) -7*a(n-5) +2*a(n-6)

k=2: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>9

k=3: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>10

k=4: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>10

k=5: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>10

k=6: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>10

k=7: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>10

Example

Some solutions for n=4 k=4
..0..1..0..2..2....0..0..2..0..2....1..1..1..1..1....1..1..1..2..2
..0..1..0..0..0....0..0..2..0..2....1..0..0..0..0....0..0..0..0..0
..0..1..0..0..0....1..0..2..0..2....2..0..0..0..0....1..1..1..1..1
..0..1..0..0..0....1..0..2..0..1....2..0..0..0..0....1..0..0..0..0
..2..2..1..1..1....2..1..2..0..1....2..0..0..0..0....2..1..1..1..0

Crossrefs

Sequence in context: A044969 A300536 A260536 * A251130 A231077 A044372

Adjacent sequences: A251134 A251135 A251136 * A251138 A251139 A251140

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 30 2014

Status

approved