A251128 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements.

10, 21, 21, 40, 40, 40, 72, 69, 69, 72, 125, 117, 108, 117, 125, 212, 193, 173, 173, 193, 212, 354, 315, 272, 266, 272, 315, 354, 585, 510, 430, 401, 401, 430, 510, 585, 960, 823, 680, 612, 580, 612, 680, 823, 960, 1568, 1326, 1080, 938, 854, 854, 938, 1080, 1326

Offset: 1

Author

R. H. Hardin, Nov 30 2014

Keywords

• nonn
• tabl

Comments

Table starts

...10...21...40...72..125..212..354..585...960..1568..2553..4148..6730.10909

...21...40...69..117..193..315..510..823..1326..2136..3442..5550..8955.14458

...40...69..108..173..272..430..680.1080..1721..2752..4413..7093.11421.18415

...72..117..173..266..401..612..938.1452..2266..3565..5646..8991.14379.23071

..125..193..272..401..580..854.1268.1912..2921..4520..7069.11153.17717.28291

..212..315..430..612..854.1214.1743.2550..3795..5747..8835.13757.21640.34309

..354..510..680..938.1268.1743.2420.3429..4957..7321.11025.16890.26241.41224

..585..823.1080.1452.1912.2550.3429.4702..6585..9447.13873.20817.31818.49369

..960.1326.1721.2266.2921.3795.4957.6585..8926.12405.17694.25890.38762.59176

.1568.2136.2752.3565.4520.5747.7321.9447.12405.16680.23037.32726.47762.71410

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1104

Crossrefs

Column 1 is A001891(n+2)

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +a(n-4)

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

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

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

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

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

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