A253510 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 2X2 and 3X3 subblock diagonal maximum minus antidiagonal minimum nondecreasing horizontally and vertically

132, 260, 260, 428, 472, 428, 636, 784, 784, 636, 884, 1196, 1332, 1196, 884, 1172, 1712, 2088, 2088, 1712, 1172, 1500, 2340, 3052, 3400, 3052, 2340, 1500, 1868, 3088, 4248, 5136, 5136, 4248, 3088, 1868, 2276, 3964, 5692, 7396, 7948, 7396, 5692, 3964

Offset

1,1

Comments

Table starts

..132..260...428...636...884..1172...1500...1868...2276...2724...3212...3740

..260..472...784..1196..1712..2340...3088...3964...4976...6132...7440...8908

..428..784..1332..2088..3052..4248...5692...7404...9404..11712..14348..17332

..636.1196..2088..3400..5136..7396..10236..13748..18024..23168..29292..36516

..884.1712..3052..5136..7948.11740..16592..22720..30300..39560..50740..64104

.1172.2340..4248..7396.11740.17888..25988..36632..50248..67508..89120.115940

.1500.3088..5692.10236.16592.25988..38564..55576..77680.106248.142556.188308

.1868.3964..7404.13748.22720.36632..55576..82200.117588.164828.226540.306780

.2276.4976..9404.18024.30300.50248..77680.117588.171236.244528.341444.469544

.2724.6132.11712.23168.39560.67508.106248.164828.244528.356736.507648.712368

Links

R. H. Hardin, Table of n, a(n) for n = 1..9378

Formula

Empirical for column k:

k=1: a(n) = 20*n^2 + 68*n + 44

k=2: a(n) = (4/3)*n^3 + 36*n^2 + (332/3)*n + 92 for n>2

k=3: a(n) = (10/3)*n^3 + 64*n^2 + (566/3)*n + 92 for n>4

k=4: a(n) = (1/3)*n^4 + 6*n^3 + (329/3)*n^2 + 288*n - 12 for n>6

k=5: a(n) = (5/6)*n^4 + 9*n^3 + (1135/6)*n^2 + 361*n - 300 for n>8

k=6: a(n) = (1/15)*n^5 + (4/3)*n^4 + (37/3)*n^3 + (1004/3)*n^2 + (1238/5)*n - 772 for n>10

k=7: a(n) = (1/6)*n^5 + (11/6)*n^4 + (97/6)*n^3 + (3661/6)*n^2 - (1501/3)*n - 980 for n>12

Example

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

Crossrefs

Sequence in context: A015235 A204649 A224548 * A253503 A195674 A319274

Adjacent sequences: A253507 A253508 A253509 * A253511 A253512 A253513

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 02 2015

Status

approved