A297802 T(n,k) = Number of n X k 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 5 neighboring 1's.

1, 1, 1, 1, 2, 1, 1, 11, 4, 1, 1, 24, 37, 7, 1, 1, 38, 100, 108, 14, 1, 1, 105, 293, 422, 533, 31, 1, 1, 381, 1320, 2195, 2936, 2434, 69, 1, 1, 1067, 6215, 16006, 23781, 17899, 10287, 155, 1, 1, 2676, 24879, 115773, 320168, 231921, 104985, 45968, 354, 1, 1, 7533, 99567

Offset

1,5

Comments

Table starts

.1...1......1.......1.........1...........1.............1...............1

.1...2.....11......24........38.........105...........381............1067

.1...4.....37.....100.......293........1320..........6215...........24879

.1...7....108.....422......2195.......16006........115773..........738989

.1..14....533....2936.....23781......320168.......4340367........46828204

.1..31...2434...17899....231921.....5511367.....123361724......2122878239

.1..69..10287..104985...2174696....91376524....3420197908.....94927605755

.1.155..45968..645568..21427001..1587468720..102189481612...4611250894511

.1.354.207906.3978117.209042911.27421636815.2993486726263.218072722004943

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) = 3*a(n-1) -2*a(n-2) +2*a(n-3) -2*a(n-4) -a(n-5),

k=3: [order 15],

k=4: [order 37],

k=5: [order 95].

Empirical for row n:

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

n=2: a(n) = 3*a(n-1) -2*a(n-2) +5*a(n-3) +6*a(n-4) -16*a(n-5) -12*a(n-6),

n=3: [order 21],

n=4: [order 55].

Example

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

Crossrefs

Column 2 is A202973.

Row 2 is A297545.

Sequence in context: A110905 A205447 A297544 * A232266 A234013 A158202

Adjacent sequences: A297799 A297800 A297801 * A297803 A297804 A297805

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 06 2018

Status

approved