A297595 T(n,k) = Number of n X k 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 5 neighboring 1s.

1, 2, 1, 3, 5, 1, 4, 9, 9, 1, 6, 13, 25, 20, 1, 9, 33, 49, 69, 41, 1, 13, 69, 145, 154, 205, 85, 1, 19, 121, 443, 752, 577, 597, 178, 1, 28, 253, 1141, 3145, 3747, 1977, 1701, 369, 1, 41, 529, 3009, 10131, 23066, 18577, 6962, 4949, 769, 1, 60, 1013, 8455, 37929, 103673

Offset: 1

Author

R. H. Hardin, Jan 01 2018

Keywords

• nonn
• tabl

Comments

Table starts

.1...2.....3.....4.......6........9........13..........19...........28

.1...5.....9....13......33.......69.......121.........253..........529

.1...9....25....49.....145......443......1141........3009.........8455

.1..20....69...154.....752.....3145.....10131.......37929.......150388

.1..41...205...577....3747....23066....103673......514290......2834897

.1..85...597..1977...18577...163704....975485.....6551844.....50398161

.1.178..1701..6962...93150..1172288...9403199....85828150....919035936

.1.369..4949.24441..464697..8419996..90862063..1120526916..16723808887

.1.769.14389.85803.2320289.60354437.875241087.14592832760.303459238317

Examples

			Some solutions for n=6 k=4
..0..0..0..0. .0..1..0..0. .1..0..0..0. .1..0..0..0. .0..0..1..0
..0..1..1..0. .0..0..1..0. .0..1..0..0. .0..1..0..0. .0..1..0..0
..0..0..0..0. .0..0..0..0. .0..1..0..0. .0..0..0..0. .0..0..0..0
..0..1..0..1. .0..0..1..1. .1..0..0..0. .0..0..0..0. .0..0..0..0
..0..1..1..1. .0..0..0..0. .1..0..0..0. .0..0..0..0. .1..0..0..0
..0..0..0..1. .1..1..0..0. .0..1..0..0. .0..0..0..0. .0..1..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..391

Crossrefs

Column 2 is A105309(n+1).

Row 1 is A000930(n+1).

Row 2 is A089977(n+1).

Formula

Empirical for column k:

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

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

k=3: a(n) = a(n-1) +2*a(n-2) +10*a(n-3) +4*a(n-4) -8*a(n-5) -8*a(n-6)

k=4: [order 9]

k=5: [order 22]

k=6: [order 40]

k=7: [order 83]

Empirical for row n:

n=1: a(n) = a(n-1) +a(n-3)

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

n=3: a(n) = a(n-1) +a(n-2) +8*a(n-3) +7*a(n-4) -8*a(n-6) -6*a(n-7)

n=4: [order 12]

n=5: [order 26]

n=6: [order 49]