A250973 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having the sum of its diagonal elements less than the absolute difference of its antidiagonal elements

14, 49, 49, 172, 308, 172, 604, 1945, 1945, 604, 2121, 12281, 22048, 12281, 2121, 7448, 77537, 249921, 249921, 77537, 7448, 26154, 489543, 2833397, 5089900, 2833397, 489543, 26154, 91841, 3090834, 32124018, 103684186, 103684186, 32124018

Offset

1,1

Comments

Table starts

....14.......49........172..........604............2121..............7448

....49......308.......1945........12281...........77537............489543

...172.....1945......22048.......249921.........2833397..........32124018

...604....12281.....249921......5089900.......103684186........2112130109

..2121....77537....2833397....103684186......3794909318......138900769559

..7448...489543...32124018...2112130109....138900769559.....9135168475316

.26154..3090834..364210219..43025963570...5084110136919...600808386292820

.91841.19514643.4129278507.876479703950.186091438754901.39514486757351514

Links

R. H. Hardin, Table of n, a(n) for n = 1..420

Formula

Empirical for column k:

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

k=2: a(n) = 8*a(n-1) -13*a(n-2) +17*a(n-3) -14*a(n-4) +3*a(n-5)

k=3: [order 9]

k=4: [order 17]

k=5: [order 31]

k=6: [order 57] for n>58

Example

Some solutions for n=3 k=4
..0..0..0..0..1....0..0..0..1..1....0..1..0..0..0....0..0..0..1..0
..0..0..0..1..1....0..1..1..0..0....0..1..1..1..1....1..1..1..0..1
..1..1..1..0..1....1..1..0..1..1....0..1..0..0..0....1..1..0..1..0
..1..1..0..1..1....0..0..1..1..0....1..1..0..0..0....0..1..0..1..1

Crossrefs

Column 1 is A010904

Sequence in context: A121202 A345691 A251228 * A039340 A043163 A043943

Adjacent sequences: A250970 A250971 A250972 * A250974 A250975 A250976

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 29 2014

Status

approved