A295213 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 3 1s.

1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 7, 10, 7, 1, 1, 14, 27, 27, 14, 1, 1, 31, 102, 147, 102, 31, 1, 1, 69, 345, 916, 916, 345, 69, 1, 1, 155, 1162, 4938, 9536, 4938, 1162, 155, 1, 1, 354, 4072, 27208, 85215, 85215, 27208, 4072, 354, 1, 1, 814, 14224, 152236, 775547, 1245294

Offset

1,5

Comments

Table starts

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

.1...2.....4......7.......14.........31...........69............155

.1...4....10.....27......102........345.........1162...........4072

.1...7....27....147......916.......4938........27208.........152236

.1..14...102....916.....9536......85215.......775547........7213161

.1..31...345...4938....85215....1245294.....18444470......278238087

.1..69..1162..27208...775547...18444470....444447937....10896495280

.1.155..4072.152236..7213161..278238087..10896495280...436106162865

.1.354.14224.848992.66719868.4170628296.265837272259.17352456088907

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

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 12]

k=4: [order 28]

k=5: [order 78]

Example

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

Crossrefs

Column 2 is A202973.

Sequence in context: A296157 A113582 A347147 * A118245 A104382 A086629

Adjacent sequences: A295210 A295211 A295212 * A295214 A295215 A295216

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 17 2017

Status

approved