A301951 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.

0, 1, 0, 1, 2, 0, 2, 5, 5, 0, 3, 16, 20, 13, 0, 5, 52, 123, 83, 34, 0, 8, 169, 680, 947, 342, 89, 0, 13, 549, 4070, 9084, 7326, 1411, 233, 0, 21, 1784, 23565, 98839, 120815, 56710, 5820, 610, 0, 34, 5797, 138014, 1029960, 2406169, 1608681, 439078, 24007, 1597, 0

Offset: 1

Author

R. H. Hardin, Mar 29 2018

Keywords

• nonn
• tabl

Comments

Table starts

.0....1.....1........2..........3............5...............8

.0....2.....5.......16.........52..........169.............549

.0....5....20......123........680.........4070...........23565

.0...13....83......947.......9084........98839.........1029960

.0...34...342.....7326.....120815......2406169........45013365

.0...89..1411....56710....1608681.....58609226......1969215107

.0..233..5820...439078...21418808...1427656268.....86143630040

.0..610.24007..3399722..285190208..34776685046...3768464135104

.0.1597.99026.26323903.3797277789.847137052736.164856325277648

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..364

Crossrefs

Column 2 is A001519.

Row 1 is A000045(n-1).

Row 2 is A232317(n-1).

Formula

Empirical for column k:

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

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

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

k=4: a(n) = 9*a(n-1) -8*a(n-2) -14*a(n-3) +4*a(n-4) +4*a(n-5) -a(n-6)

k=5: [order 13] for n>15

k=6: [order 26] for n>28

k=7: [order 43] for n>47

Empirical for row n:

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

n=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4) for n>6

n=3: [order 10] for n>12

n=4: [order 36] for n>40