A300776 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 4, 3, 4, 0, 0, 9, 11, 11, 9, 0, 0, 19, 32, 36, 32, 19, 0, 0, 41, 102, 179, 179, 102, 41, 0, 0, 88, 330, 735, 1536, 735, 330, 88, 0, 0, 189, 1059, 3482, 10374, 10374, 3482, 1059, 189, 0, 0, 406, 3418, 15986, 78932, 116954, 78932, 15986, 3418

Offset: 1

Author

R. H. Hardin, Mar 12 2018

Keywords

• nonn
• tabl

Comments

Table starts

.0...0....0.....0.......0.........0...........0............0..............0

.0...1....2.....4.......9........19..........41...........88............189

.0...2....3....11......32.......102.........330.........1059...........3418

.0...4...11....36.....179.......735........3482........15986..........74347

.0...9...32...179....1536.....10374.......78932.......592064........4449947

.0..19..102...735...10374....116954.....1413931.....17336190......210669938

.0..41..330..3482...78932...1413931....27354464....538564737....10457318118

.0..88.1059.15986..592064..17336190...538564737..16992197390...534677180915

.0.189.3418.74347.4449947.210669938.10457318118.534677180915.27071152148341

Examples

			Some solutions for n=5 k=4
..0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..0..0. .0..0..1..1
..0..0..1..1. .0..1..1..1. .0..1..1..1. .0..1..1..0. .0..1..1..1
..0..0..1..0. .1..0..0..1. .0..1..1..1. .0..1..0..1. .0..0..0..0
..1..1..0..0. .1..0..0..1. .0..0..0..1. .0..0..1..1. .0..0..0..0
..1..0..0..0. .1..1..1..1. .0..0..1..1. .0..1..1..1. .0..0..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..219

Crossrefs

Column 2 is A078039(n-2).

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3)

k=3: [order 15]

k=4: [order 56] for n>57