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A253004 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 within 3 of its king move distance from the upper left 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, 14, 1, 1, 14, 10, 20, 55, 34, 1, 34, 55, 20, 35, 140, 279, 69, 69, 279, 140, 35, 56, 285, 1028, 1132, 69, 1132, 1028, 285, 56, 84, 506, 2601, 7235, 3072, 3072, 7235, 2601, 506, 84, 120, 819, 5318, 25233, 39758, 3072 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,11

COMMENTS

Table starts

..0...0....0......1.......4.......10........20.........35.........56.........84

..0...0....0......1......14.......55.......140........285........506........819

..0...0....0......1......34......279......1028.......2601.......5318.......9499

..1...1....1......1......69.....1132......7235......25233......63135.....129133

..4..14...34.....69......69.....3072.....39758.....228484.....775433....1932763

.10..55..279...1132....3072.....3072....122833....1486152....8270017...27983105

.20.140.1028...7235...39758...122833....122833....4915726...59154789..329035981

.35.285.2601..25233..228484..1486152...4915726....4915726..204051186.2492354946

.56.506.5318..63135..775433..8270017..59154789..204051186..204051186.8849413857

.84.819.9499.129133.1932763.27983105.329035981.2492354946.8849413857.8849413857

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..1200

FORMULA

Empirical for column k:

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

k=2: a(n) = (8/3)*n^3 - 26*n^2 + (253/3)*n - 91 for n>2

k=3: a(n) = (160/3)*n^3 - 708*n^2 + (9539/3)*n - 4831 for n>4

k=4: a(n) = (4096/3)*n^3 - 22816*n^2 + (388490/3)*n - 249567 for n>6

k=5: a(n) = (133120/3)*n^3 - 893616*n^2 + (18332582/3)*n - 14187577 for n>8

k=6: a(n) = (5242880/3)*n^3 - 41275392*n^2 + (991610656/3)*n - 897487301 for n>10

k=7: a(n) = (235012096/3)*n^3 - 2126491008*n^2 + (58625640404/3)*n - 60801081325 for n>12

EXAMPLE

Some solutions for n=6 k=4

..0..0..1..2....0..0..1..2....0..0..1..2....0..0..1..1....0..0..1..1

..0..0..1..2....1..1..1..2....0..0..1..2....0..0..1..1....0..1..1..1

..1..1..1..2....1..1..2..2....0..0..1..2....0..1..1..2....1..1..1..1

..1..1..2..2....2..2..2..2....0..1..1..2....1..1..1..2....1..1..1..2

..2..2..2..2....2..2..2..2....1..1..1..2....1..1..1..2....1..2..2..2

..2..2..2..2....2..2..2..2....2..2..2..2....2..2..2..2....2..2..2..2

CROSSREFS

Column 1 is A000292(n-3)

Column 2 is A100157(n-3)

Sequence in context: A070432 A170989 A290457 * A253011 A290456 A010639

Adjacent sequences:  A253001 A253002 A253003 * A253005 A253006 A253007

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 25 2014

STATUS

approved

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Last modified October 23 19:37 EDT 2019. Contains 328373 sequences. (Running on oeis4.)