A295120 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 4 1s.

1, 2, 2, 3, 5, 3, 4, 9, 9, 4, 6, 20, 26, 20, 6, 9, 41, 77, 77, 41, 9, 13, 85, 226, 326, 226, 85, 13, 19, 178, 665, 1373, 1373, 665, 178, 19, 28, 369, 1960, 5793, 8257, 5793, 1960, 369, 28, 41, 769, 5769, 24347, 49302, 49302, 24347, 5769, 769, 41, 60, 1600, 16983, 102398

Offset

1,2

Comments

Table starts

..1...2.....3......4........6.........9.........13...........19............28

..2...5.....9.....20.......41........85........178..........369...........769

..3...9....26.....77......226.......665.......1960.........5769.........16983

..4..20....77....326.....1373......5793......24347.......102398........431050

..6..41...226...1373.....8257.....49302.....295083......1768323......10586331

..9..85...665...5793....49302....420519....3590821.....30650456.....261518933

.13.178..1960..24347...295083...3590821...43655680....530696748....6452840307

.19.369..5769.102398..1768323..30650456..530696748...9196006628..159316011413

.28.769.16983.431050.10586331.261518933.6452840307.159316011413.3931962260999

Links

R. H. Hardin, Table of n, a(n) for n = 1..391

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) +a(n-3) -a(n-4)

k=3: [order 10]

k=4: [order 14]

k=5: [order 40]

k=6: [order 78]

Example

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

Crossrefs

Column 1 is A000930(n+1).

Column 2 is A105309(n+1).

Sequence in context: A225622 A196436 A197199 * A196957 A124727 A210565

Adjacent sequences: A295117 A295118 A295119 * A295121 A295122 A295123

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 15 2017

Status

approved