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

1,5

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

Links

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

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

Example

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

Crossrefs

Column 2 is A001519.

Row 1 is A000045(n-1).

Row 2 is A232317(n-1).

Sequence in context: A133394 A305628 A094721 * A144529 A319498 A349782

Adjacent sequences: A301948 A301949 A301950 * A301952 A301953 A301954

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 29 2018

Status

approved