A303410 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

0, 1, 0, 1, 3, 0, 2, 7, 10, 0, 3, 10, 28, 23, 0, 5, 27, 42, 119, 61, 0, 8, 45, 100, 168, 541, 162, 0, 13, 98, 290, 547, 902, 2327, 421, 0, 21, 193, 730, 2079, 4013, 3256, 10384, 1103, 0, 34, 379, 1700, 6322, 29411, 21361, 15852, 47491, 2890, 0, 55, 778, 4246, 17903

Offset: 1

Author

R. H. Hardin, Apr 23 2018

Keywords

• nonn
• tabl

Comments

Table starts

.0....1......1......2.......3.........5..........8..........13............21

.0....3......7.....10......27........45.........98.........193...........379

.0...10.....28.....42.....100.......290........730........1700..........4246

.0...23....119....168.....547......2079.......6322.......17903.........53665

.0...61....541....902....4013.....29411.....160247......660748.......3071197

.0..162...2327...3256...21361....236326....1716995.....8688851......56229035

.0..421..10384..15852..115770...2158662...24386918...158640643....1293822589

.0.1103..47491..77904..803911..27002794..497878411..4298730424...50946692110

.0.2890.208616.314276.4667376.250400003.6748940959.74532460229.1222253462556

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..180

Crossrefs

Column 2 is A185828.

Column 4 is A302524.

Row 1 is A000045(n-1).

Row 2 is A302279.

Row 3 is A302529.

Formula

Empirical for column k:

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

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

k=3: [order 18]

k=4: [order 72]

Empirical for row n:

n=1: a(n) = a(n-1) +a(n-2)

n=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5

n=3: [order 15] for n>17

n=4: [order 71] for n>72