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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 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified June 13 00:57 EDT 2021. Contains 344980 sequences. (Running on oeis4.)