A295943 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1 or 3 king-move neighboring 1s.

1, 2, 2, 3, 8, 3, 4, 15, 15, 4, 6, 33, 41, 33, 6, 9, 104, 120, 120, 104, 9, 13, 228, 465, 534, 465, 228, 13, 19, 529, 1472, 2976, 2976, 1472, 529, 19, 28, 1469, 4667, 13759, 29081, 13759, 4667, 1469, 28, 41, 3442, 16230, 65009, 187960, 187960, 65009, 16230, 3442

Offset

1,2

Comments

Table starts

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

..2....8....15......33......104........228.........529..........1469

..3...15....41.....120......465.......1472........4667.........16230

..4...33...120.....534.....2976......13759.......65009........325008

..6..104...465....2976....29081.....187960.....1311947......10551008

..9..228..1472...13759...187960....1806751....18443146.....209884397

.13..529..4667...65009..1311947...18443146...279143247....4651767361

.19.1469.16230..325008.10551008..209884397..4651767361..117889600265

.28.3442.53266.1565481.75078015.2194039726.71601077879.2659460386138

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) +a(n-2) +9*a(n-3) -4*a(n-4) -4*a(n-5) -4*a(n-6)

k=3: [order 9]

k=4: [order 21]

k=5: [order 55]

Example

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

Crossrefs

Column 1 is A000930(n+1).

Sequence in context: A110985 A153216 A327259 * A296804 A296952 A141611

Adjacent sequences: A295940 A295941 A295942 * A295944 A295945 A295946

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 30 2017

Status

approved