A295551 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 3 or 4 1s.

1, 2, 2, 3, 5, 3, 4, 11, 11, 4, 6, 24, 34, 24, 6, 9, 55, 116, 116, 55, 9, 13, 123, 391, 598, 391, 123, 13, 19, 276, 1304, 3035, 3035, 1304, 276, 19, 28, 621, 4374, 15352, 23315, 15352, 4374, 621, 28, 41, 1395, 14645, 78434, 179499, 179499, 78434, 14645, 1395, 41, 60

Offset

1,2

Comments

Table starts

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

..2....5....11......24.......55........123..........276...........621

..3...11....34.....116......391.......1304.........4374.........14645

..4...24...116.....598.....3035......15352........78434........399324

..6...55...391....3035....23315.....179499......1385901......10668635

..9..123..1304...15352...179499....2094347.....24486926.....286066769

.13..276..4374...78434..1385901...24486926....434357928....7703929911

.19..621.14645..399324.10668635..286066769...7703929911..207301696580

.28.1395.49051.2032606.82245065.3346911102.136731507572.5581805664324

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +2*a(n-2) +2*a(n-3) -a(n-5)

k=3: [order 17]

k=4: [order 45]

Example

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

Crossrefs

Column 1 is A000930(n+1).

Column 2 is A295091.

Sequence in context: A209568 A227641 A295097 * A196696 A196729 A197069

Adjacent sequences: A295548 A295549 A295550 * A295552 A295553 A295554

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 23 2017

Status

approved