A300605 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 10, 6, 10, 1, 1, 13, 18, 18, 13, 1, 1, 42, 23, 42, 23, 42, 1, 1, 74, 89, 141, 141, 89, 74, 1, 1, 188, 230, 394, 615, 394, 230, 188, 1, 1, 387, 552, 1397, 2394, 2394, 1397, 552, 387, 1, 1, 885, 1555, 4808, 11752, 16629, 11752, 4808, 1555, 885, 1, 1

Offset

1,5

Comments

Table starts

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

.1...3....2....10.....13......42.......74........188.........387..........885

.1...2....6....18.....23......89......230........552........1555.........4206

.1..10...18....42....141.....394.....1397.......4808.......16894........58420

.1..13...23...141....615....2394....11752......56417......267220......1288938

.1..42...89...394...2394...16629...110249.....729292.....4931949.....33688331

.1..74..230..1397..11752..110249..1056816....9684995....92435041....880584819

.1.188..552..4808..56417..729292..9684995..125507384..1674738412..22241403689

.1.387.1555.16894.267220.4931949.92435041.1674738412.31211394832.583083792885

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

k=2: a(n) = 4*a(n-2) +2*a(n-3) +a(n-5) -3*a(n-6) +a(n-7)

k=3: [order 30] for n>31

Example

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

Crossrefs

Column 2 is A300374.

Sequence in context: A143214 A300380 A300682 * A301330 A175636 A352935

Adjacent sequences: A300602 A300603 A300604 * A300606 A300607 A300608

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 09 2018

Status

approved