A253011 T(n,k)=Number of nXk nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value increasing by 0 or 1 with every step right, diagonally se or down

0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 4, 1, 0, 1, 4, 10, 19, 1, 1, 19, 10, 20, 85, 54, 1, 54, 85, 20, 35, 231, 632, 124, 124, 632, 231, 35, 56, 489, 2902, 3423, 250, 3423, 2902, 489, 56, 84, 891, 8416, 33533, 14795, 14795, 33533, 8416, 891, 84, 120, 1469, 18770, 158877, 309990

Offset

1,11

Comments

Table starts

..0....0.....0.......1........4.........10..........20............35

..0....0.....0.......1.......19.........85.........231...........489

..0....0.....0.......1.......54........632........2902..........8416

..1....1.....1.......1......124.......3423.......33533........158877

..4...19....54.....124......250......14795......309990.......2853292

.10...85...632....3423....14795......54219.....2327062......43197859

.20..231..2902...33533...309990....2327062....14697256.....541365583

.35..489..8416..158877..2853292...43197859...541365583....5713126349

.56..891.18770..490403.14125312..395069496..9617848524..196919486736

.84.1469.35564.1156178.46481352.2063349297.90094114144.3496191411901

Links

R. H. Hardin, Table of n, a(n) for n = 1..480

Formula

Empirical for column k:

k=1: a(n) = (1/6)*n^3 - 1*n^2 + (11/6)*n - 1

k=2: a(n) = (16/3)*n^3 - 56*n^2 + (590/3)*n - 231 for n>3

k=3: a(n) = (800/3)*n^3 - 3980*n^2 + (60442/3)*n - 34576 for n>6

k=4: a(n) = (65536/3)*n^3 - 422912*n^2 + (8343128/3)*n - 6208382 for n>9

k=5: a(n) = 2973696*n^3 - 70716096*n^2 + 570494664*n - 1560617160 for n>12

k=6: [polynomial of degree 3] for n>15

k=7: [polynomial of degree 3] for n>18

Example

Some solutions for n=6 k=4
..0..0..1..1....0..0..0..1....0..0..1..2....0..0..0..1....0..0..0..0
..0..0..1..2....1..1..1..1....1..1..1..2....0..0..0..1....0..0..0..0
..1..1..1..2....1..1..2..2....1..1..1..2....0..0..0..1....0..0..0..1
..1..1..1..2....1..1..2..2....1..1..1..2....0..0..0..1....0..1..1..1
..1..1..1..2....1..2..2..2....1..2..2..2....0..0..1..1....1..1..2..2
..2..2..2..2....2..2..2..2....1..2..2..2....1..1..1..2....1..1..2..2

Crossrefs

Column 1 is A000292(n-3)

Column 2 is A063496(n-3)

Sequence in context: A344851 A346202 A253004 * A290456 A010639 A035588

Adjacent sequences: A253008 A253009 A253010 * A253012 A253013 A253014

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 25 2014

Status

approved