A253456 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically

81, 414, 414, 1388, 1975, 1388, 3639, 4782, 4782, 3639, 8501, 8554, 7782, 8554, 8501, 19701, 15220, 11147, 11147, 15220, 19701, 48293, 31630, 19254, 15730, 19254, 31630, 48293, 126357, 74324, 39463, 26831, 26831, 39463, 74324, 126357, 346997, 188438

Offset

1,1

Comments

Table starts

.....81.....414....1388....3639....8501...19701...48293..126357...346997

....414....1975....4782....8554...15220...31630...74324..188438...502364

...1388....4782....7782...11147...19254...39463...89556..218326...561564

...3639....8554...11147...15730...26831...52912..114717..266911...656997

...8501...15220...19254...26831...44242...83003..170184..373130...864720

..19701...31630...39463...52912...83003..147332..285681..590963..1287225

..48293...74324...89556..114717..170184..285681..526430.1036512..2142374

.126357..188438..218326..266911..373130..590963.1036512.1956194..3881256

.346997..502364..561564..656997..864720.1287225.2142374.3881256..7444718

.982677.1387310.1505134.1694263.2104994.2936843.4611192.7988474.14828736

Links

R. H. Hardin, Table of n, a(n) for n = 1..364

Formula

Empirical for column k:

k=1: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>10

k=2..9: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>9

Empirical for column k:

k=1: a(n) = 400*3^(n-3) + 205*2^(n-1) + 2917 for n>7

k=2: a(n) = 529*3^(n-3) + 444*2^(n-1) + 3059 for n>6

k=3: a(n) = 529*3^(n-3) + 673*2^(n-1) + 3635 for n>6

k=4: a(n) = 529*3^(n-3) + 1039*2^(n-1) + 5372 for n>6

k=5: a(n) = 529*3^(n-3) + 1832*2^(n-1) + 10087 for n>6

k=6: a(n) = 529*3^(n-3) + 3431*2^(n-1) + 23248 for n>6

k=7: a(n) = 529*3^(n-3) + 6631*2^(n-1) + 59197 for n>6

k=8: a(n) = 529*3^(n-3) + 13031*2^(n-1) + 159679 for n>6

k=9: a(n) = 529*3^(n-3) + 25831*2^(n-1) + 446341 for n>6

Example

Some solutions for n=4 k=4
..0..1..2..2..2....0..2..1..2..1....0..1..1..1..1....1..2..0..0..1
..0..0..1..1..1....2..2..1..2..1....2..2..2..2..2....1..2..0..0..1
..1..0..1..1..1....2..2..1..2..1....2..1..1..1..1....1..2..0..0..1
..1..0..1..1..1....1..1..0..1..0....1..0..0..0..1....1..2..0..0..1
..1..0..1..1..2....1..1..0..1..0....1..0..0..0..2....1..2..0..0..1

Crossrefs

Sequence in context: A357015 A102741 A253495 * A236155 A253449 A236148

Adjacent sequences: A253453 A253454 A253455 * A253457 A253458 A253459

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 01 2015

Status

approved