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

Author

R. H. Hardin, Dec 22 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000124(n-1)

Column 2 is A078370(n-2)

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