A252836 T(n,k)=Number of nXk nonnegative integer arrays with upper left 0 and every value within 2 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

1, 2, 2, 4, 5, 4, 7, 13, 13, 7, 11, 29, 44, 29, 11, 16, 53, 127, 127, 53, 16, 22, 85, 288, 493, 288, 85, 22, 29, 125, 529, 1474, 1474, 529, 125, 29, 37, 173, 850, 3365, 6068, 3365, 850, 173, 37, 46, 229, 1251, 6211, 18528, 18528, 6211, 1251, 229, 46, 56, 293, 1732, 10017

Offset

1,2

Comments

Table starts

..1...2....4.....7.....11......16.......22........29........37.........46

..2...5...13....29.....53......85......125.......173.......229........293

..4..13...44...127....288.....529......850......1251......1732.......2293

..7..29..127...493...1474....3365.....6211.....10017.....14783......20509

.11..53..288..1474...6068...18528....42738.....79563....129173.....191583

.16..85..529..3365..18528...78674...244131....569420...1070036....1750150

.22.125..850..6211..42738..244131..1056756...3320837...7822881...14827629

.29.173.1251.10017..79563..569420..3320837..14564701..46222275..109796227

.37.229.1732.14783.129173.1070036..7822881..46222275.204666202..654583926

.46.293.2293.20509.191583.1750150.14827629.109796227.654583926.2919462498

Links

R. H. Hardin, Table of n, a(n) for n = 1..1135

Formula

Empirical for column k:

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

k=2: a(n) = 4*n^2 - 12*n + 13 for n>1

k=3: a(n) = 40*n^2 - 199*n + 283 for n>3

k=4: a(n) = 480*n^2 - 3394*n + 6449 for n>5

k=5: a(n) = 6400*n^2 - 59190*n + 143483 for n>7

k=6: a(n) = 90112*n^2 - 1032064*n + 3059590 for n>9

k=7: a(n) = 1306624*n^2 - 17846996*n + 62638467 for n>11

Example

Some solutions for n=4 k=4
..0..1..2..2....0..1..1..2....0..0..1..1....0..0..1..1....0..0..1..1
..1..1..2..2....0..1..1..2....1..1..1..1....0..1..1..1....1..1..1..1
..1..1..2..3....1..1..2..2....1..1..2..2....0..1..1..1....1..1..1..1
..1..2..2..3....1..1..2..2....1..2..2..3....1..1..2..2....1..1..2..2

Crossrefs

Column 1 is A000124(n-1)

Column 2 is A078370(n-2)

Sequence in context: A128900 A136099 A210597 * A286101 A072454 A115216

Adjacent sequences: A252833 A252834 A252835 * A252837 A252838 A252839

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 22 2014

Status

approved