A295205 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 4 1s.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 8, 4, 1, 1, 6, 14, 14, 6, 1, 1, 9, 25, 42, 25, 9, 1, 1, 13, 53, 108, 108, 53, 13, 1, 1, 19, 111, 284, 438, 284, 111, 19, 1, 1, 28, 217, 777, 1597, 1597, 777, 217, 28, 1, 1, 41, 426, 2146, 5831, 8241, 5831, 2146, 426, 41, 1, 1, 60, 860, 5887

Offset

1,5

Comments

Table starts

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

.1..2...3....4.....6.......9.......13........19.........28..........41

.1..3...8...14....25......53......111.......217........426.........860

.1..4..14...42...108.....284......777......2146.......5887.......16061

.1..6..25..108...438....1597.....5831.....21717......81590......307267

.1..9..53..284..1597....8241....40924....205338....1042704.....5314555

.1.13.111..777..5831...40924...279663...1900344...12981261....89115875

.1.19.217.2146.21717..205338..1900344..17574795..162114347..1498926338

.1.28.426.5887.81590.1042704.12981261.162114347.2023191364.25252046266

Links

R. H. Hardin, Table of n, a(n) for n = 1..311

Formula

Empirical for column k:

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

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

k=3: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) +a(n-4) -2*a(n-5)

k=4: [order 13]

k=5: [order 32]

k=6: [order 85]

Example

Some solutions for n=6 k=4
..0..1..1..0. .1..1..1..0. .0..1..1..0. .0..1..1..1. .1..1..1..0
..0..1..1..0. .1..0..1..0. .0..1..1..0. .0..1..0..1. .1..0..1..1
..0..0..0..0. .1..0..1..0. .0..0..0..0. .0..1..0..1. .1..1..0..1
..0..0..1..1. .1..0..1..0. .0..0..1..1. .1..1..0..1. .0..1..0..1
..0..0..1..1. .1..0..1..0. .0..1..1..1. .1..0..1..1. .0..1..0..1
..0..0..0..0. .1..1..1..0. .0..1..1..0. .1..1..1..0. .0..1..1..1

Crossrefs

Column 2 is A000930(n+1).

Sequence in context: A202756 A156354 A378938 * A297020 A099597 A358146

Adjacent sequences: A295202 A295203 A295204 * A295206 A295207 A295208

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 16 2017

Status

approved