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

1,5

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

Links

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

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

Example

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

Crossrefs

Column 2 is A185828.

Column 4 is A302524.

Row 1 is A000045(n-1).

Row 2 is A302279.

Row 3 is A302529.

Sequence in context: A302278 A302728 A302528 * A126671 A209437 A325447

Adjacent sequences: A303407 A303408 A303409 * A303411 A303412 A303413

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 23 2018

Status

approved