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

1,2

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

Links

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

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]

Example

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

Crossrefs

Column 2 is A105309(n+1).

Row 1 is A000930(n+1).

Row 2 is A089977(n+1).

Sequence in context: A188211 A175009 A297395 * A049069 A030237 A210557

Adjacent sequences: A297592 A297593 A297594 * A297596 A297597 A297598

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 01 2018

Status

approved