A302728 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4 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, 22, 23, 0, 5, 27, 29, 83, 61, 0, 8, 45, 74, 89, 301, 162, 0, 13, 98, 162, 287, 353, 1079, 421, 0, 21, 193, 363, 689, 1307, 941, 4064, 1103, 0, 34, 379, 782, 1723, 4505, 4491, 3316, 15183, 2890, 0, 55, 778, 1766, 4491, 16265, 20842, 17828

Offset

1,5

Comments

Table starts

.0....1.....1.....2......3.......5........8........13........21.........34

.0....3.....7....10.....27......45.......98.......193.......379........778

.0...10....22....29.....74.....162......363.......782......1766.......3953

.0...23....83....89....287.....689.....1723......4491.....10433......28009

.0...61...301...353...1307....4505....16265.....46773....136935.....481479

.0..162..1079...941...4491...20842....89121....286746...1022779....4520360

.0..421..4064..3316..17828..104969...532511...1932168...7608792...40495097

.0.1103.15183.12016..80293..623549..4281120..17200486..81226394..547173278

.0.2890.55012.34060.304958.3195095.26823700.120221024.683140749.5901256655

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

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 16]

k=4: [order 72] for n>73

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 16] for n>18

n=4: [order 68] for n>69

Example

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

Crossrefs

Column 2 is A185828.

Column 4 is A302274.

Row 1 is A000045(n-1).

Row 2 is A302279.

Row 3 is A302280.

Sequence in context: A085550 A223139 A302278 * A302528 A303410 A126671

Adjacent sequences: A302725 A302726 A302727 * A302729 A302730 A302731

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 12 2018

Status

approved