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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 7
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 (list; table; graph; refs; listen; history; text; internal format)
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: A170989 A290457 A253004 * A290456 A010639 A035588

Adjacent sequences:  A253008 A253009 A253010 * A253012 A253013 A253014

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 25 2014

STATUS

approved

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Last modified October 13 19:52 EDT 2019. Contains 327981 sequences. (Running on oeis4.)