A258554 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically

16, 44, 44, 104, 112, 104, 228, 210, 296, 228, 480, 344, 598, 652, 480, 988, 506, 985, 1244, 1329, 988, 2008, 683, 1403, 1891, 2384, 2530, 2008, 4052, 894, 1917, 2509, 3754, 3980, 4667, 4052, 8144, 1140, 2542, 3314, 5070, 6196, 6348, 8419, 8144, 16332, 1421

Offset

1,1

Comments

Table starts

....16....44...104...228...480...988..2008..4052..8144..16332..32712..65476

....44...112...210...344...506...683...894..1140..1421...1725...2071...2460

...104...296...598...985..1403..1917..2542..3222..3940...4767...5718...6737

...228...652..1244..1891..2509..3314..4313..5356..6331...7470...8820..10231

...480..1329..2384..3754..5070..6662..8612.10720.12831..15045..17532..20200

...988..2530..3980..6196..8339.10854.13833.17058.20414..23858..27446..31237

..2008..4667..6348..9688.12940.16942.21653.26628.31806..37351..43158..49004

..4052..8419..9567.14216.18630.24300.31254.38451.45713..53599..62205..70891

..8144.14932.13847.20285.26240.33844.43655.54137.64507..75625..87878.100660

.16332.26184.19227.27687.35386.45166.57928.71823.85853.100830.116939.133789

Links

R. H. Hardin, Table of n, a(n) for n = 1..8053

Formula

Empirical for column k:

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

k=2: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +3*a(n-4) -4*a(n-5) +2*a(n-6) +2*a(n-7) -3*a(n-8) +a(n-9) for n>11

k=3: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -4*a(n-5) +6*a(n-6) -4*a(n-7) +a(n-8) for n>11

k=4: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -4*a(n-5) +6*a(n-6) -4*a(n-7) +a(n-8) for n>12

k=5: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -4*a(n-5) +6*a(n-6) -4*a(n-7) +a(n-8) for n>13

k=6: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -4*a(n-5) +6*a(n-6) -4*a(n-7) +a(n-8) for n>14

k=7: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -4*a(n-5) +6*a(n-6) -4*a(n-7) +a(n-8) for n>15

Empirical for row n:

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

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

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

n=4: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7) for n>11

n=5: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7) for n>12

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

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

Example

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

Crossrefs

Sequence in context: A316636 A187721 A253397 * A253326 A204039 A235413

Adjacent sequences: A258551 A258552 A258553 * A258555 A258556 A258557

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 03 2015

Status

approved