A251201 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having the minimum of its diagonal elements less than the absolute difference of its antidiagonal elements

10, 25, 25, 64, 86, 64, 164, 310, 310, 164, 421, 1135, 1654, 1135, 421, 1081, 4172, 8976, 8976, 4172, 1081, 2776, 15353, 49104, 73170, 49104, 15353, 2776, 7129, 56519, 268638, 599869, 599869, 268638, 56519, 7129, 18308, 208082, 1470646, 4923412

Offset

1,1

Comments

Table starts

....10......25........64.........164...........421............1081

....25......86.......310........1135..........4172...........15353

....64.....310......1654........8976.........49104..........268638

...164....1135......8976.......73170........599869.........4923412

...421....4172.....49104......599869.......7392190........91120318

..1081...15353....268638.....4923412......91120318......1688254298

..2776...56519...1470646....40413851....1123772109.....31288421074

..7129..208082...8050116...331748759...13857491196....579864211963

.18308..766105..44068836..2723267431..170891121600..10746714294838

.47017.2820622.241240750.22354871755.2107379861537.199169443650957

Links

R. H. Hardin, Table of n, a(n) for n = 1..799

Formula

Empirical for column k:

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

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

k=3: [order 9] for n>10

k=4: [order 14] for n>16

k=5: [order 22] for n>25

k=6: [order 35] for n>39

k=7: [order 56] for n>61

Example

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

Crossrefs

Sequence in context: A180043 A225974 A251317 * A048195 A133634 A174051

Adjacent sequences: A251198 A251199 A251200 * A251202 A251203 A251204

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 30 2014

Status

approved