A253495 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally

81, 414, 414, 1388, 1377, 1388, 3639, 3090, 2640, 3639, 8501, 5386, 4196, 4720, 8501, 19701, 9679, 6476, 6931, 9654, 19701, 48293, 20975, 11937, 10477, 13528, 22236, 48293, 126357, 51167, 25715, 18526, 19475, 29370, 55362, 126357, 346997, 133311

Offset

1,1

Comments

Table starts

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

....414....1377....3090....5386....9679...20975...51167..133311...362399

...1388....2640....4196....6476...11937...25715...60586..151946...399466

...3639....4720....6931...10477...18526...37469...82676..194708...483572

...8501....9654...13528...19475...32652...61955..127898..281402...653210

..19701...22236...29370...40117...63550..113573..220988..457436...995132

..48293...55362...68992...89339..133284..224747..415106..817442..1686914

.126357..145428..172050..211597..296566..470909..827156.1561268..3094292

.346997..397002..449608..527555..694572.1034675.1722698.3120362..5980490

.982677.1114476.1219050.1373797.1704910.2376533.3728108.6452876.11967212

Links

R. H. Hardin, Table of n, a(n) for n = 1..362

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

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

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

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

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

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

Empirical for row n:

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

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

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

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

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

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

n=7: 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) = 49*3^(n-1) + 291*2^(n-1) + 1017 for n>5

k=3: a(n) = 49*3^(n-1) + 494*2^(n-1) + 1655 for n>4

k=4: a(n) = 49*3^(n-1) + 794*2^(n-1) + 2802 for n>3

k=5: a(n) = 49*3^(n-1) + 1435*2^(n-1) + 5723 for n>3

k=6: a(n) = 49*3^(n-1) + 2730*2^(n-1) + 14306 for n>3

k=7: a(n) = 49*3^(n-1) + 5322*2^(n-1) + 38777 for n>3

k=8: a(n) = 49*3^(n-1) + 10506*2^(n-1) + 109337 for n>3

k=9: a(n) = 49*3^(n-1) + 20874*2^(n-1) + 315257 for n>3

Empirical for row n:

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

n=2: a(n) = 400*3^(n-3) + 271*2^(n-1) + 1423 for n>6

n=3: a(n) = 400*3^(n-3) + 415*2^(n-1) + 1626 for n>6

n=4: a(n) = 400*3^(n-3) + 738*2^(n-1) + 3044 for n>6

n=5: a(n) = 400*3^(n-3) + 1386*2^(n-1) + 6794 for n>6

n=6: a(n) = 400*3^(n-3) + 2682*2^(n-1) + 16940 for n>6

n=7: a(n) = 400*3^(n-3) + 5274*2^(n-1) + 45170 for n>6

n=8: a(n) = 400*3^(n-3) + 10458*2^(n-1) + 125444 for n>6

n=9: a(n) = 400*3^(n-3) + 20826*2^(n-1) + 357434 for n>6

Example

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

Crossrefs

Column 1 and row 1 are A253449

Sequence in context: A237176 A357015 A102741 * A253456 A236155 A253449

Adjacent sequences: A253492 A253493 A253494 * A253496 A253497 A253498

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 02 2015

Status

approved