A297544 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 or 3 neighboring 1s.

1, 1, 1, 1, 2, 1, 1, 11, 4, 1, 1, 24, 35, 7, 1, 1, 38, 93, 88, 14, 1, 1, 105, 197, 275, 461, 31, 1, 1, 381, 905, 1233, 2205, 2050, 69, 1, 1, 1067, 4617, 10234, 12161, 13248, 8057, 155, 1, 1, 2676, 17190, 65363, 205888, 94647, 67215, 35640, 354, 1, 1, 7533, 60751, 355573

Offset

1,5

Comments

Table starts

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

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

.1...4.....35......93......197.........905..........4617..........17190

.1...7.....88.....275.....1233.......10234.........65363.........355573

.1..14....461....2205....12161......205888.......2748026.......25141813

.1..31...2050...13248....94647.....3015179......67372651......916902295

.1..69...8057...67215...754342....45293985....1610981344....33425081735

.1.155..35640..401415..6315609...726450667...45496070039..1479214192234

.1.354.158090.2403621.51451261.11267743659.1204223924807.59920115456355

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

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 14]

k=4: [order 22]

k=5: [order 54]

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 17]

n=4: [order 40]

Example

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

Crossrefs

Column 2 is A202973.

Sequence in context: A260950 A110905 A205447 * A297802 A232266 A234013

Adjacent sequences: A297541 A297542 A297543 * A297545 A297546 A297547

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 31 2017

Status

approved