A252938 T(n,k)=Number of nXk nonnegative integer arrays with upper left 0 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.

1, 2, 2, 4, 5, 4, 8, 13, 13, 8, 15, 34, 44, 34, 15, 26, 83, 153, 153, 83, 26, 42, 176, 494, 711, 494, 176, 42, 64, 329, 1343, 3067, 3067, 1343, 329, 64, 93, 558, 3016, 10920, 17962, 10920, 3016, 558, 93, 130, 879, 5833, 30818, 86488, 86488, 30818, 5833, 879, 130, 176

Offset: 1

Author

R. H. Hardin, Dec 24 2014

Keywords

• nonn
• tabl

Comments

Table starts

...1....2.....4......8......15.......26.........42..........64...........93

...2....5....13.....34......83......176........329.........558..........879

...4...13....44....153.....494.....1343.......3016........5833........10114

...8...34...153....711....3067....10920......30818.......70640.......138558

..15...83...494...3067...17962....86488.....320270......917811......2127013

..26..176..1343..10920...86488...578342....2952734....11219797.....32649081

..42..329..3016..30818..320270..2952734...21312696...113154831....440052087

..64..558..5833..70640..917811.11219797..113154831...857248091...4687944300

..93..879.10114.138558.2127013.32649081..440052087..4687944300..36723156004

.130.1308.16179.242764.4211511.76641323.1302939451.18615501830.205553855458

Examples

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

Links

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

Crossrefs

Column 1 is A000125(n-1)

Formula

Empirical for column k:

k=1: a(n) = (1/6)*n^3 - (1/2)*n^2 + (4/3)*n

k=2: a(n) = (8/3)*n^3 - 18*n^2 + (145/3)*n - 42 for n>2

k=3: a(n) = (160/3)*n^3 - 548*n^2 + (6071/3)*n - 2591 for n>4

k=4: a(n) = (4096/3)*n^3 - 18720*n^2 + (269642/3)*n - 149376 for n>6

k=5: a(n) = (133120/3)*n^3 - 760496*n^2 + (13526246/3)*n - 9199709 for n>8

k=6: [polynomial of degree 3] for n>10

k=7: [polynomial of degree 3] for n>12