A296554 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 3 or 6 neighboring 1s.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 4, 5, 4, 1, 1, 1, 1, 5, 7, 7, 5, 1, 1, 1, 1, 7, 10, 11, 10, 7, 1, 1, 1, 1, 10, 17, 18, 18, 17, 10, 1, 1, 1, 1, 14, 28, 34, 32, 34, 28, 14, 1, 1, 1, 1, 19, 43, 59, 62, 62, 59, 43, 19, 1, 1, 1, 1, 26, 66, 100, 118, 148, 118, 100, 66, 26

Offset

1,13

Comments

Table starts

.1.1..1..1...1...1...1....1....1.....1.....1......1......1.......1.......1

.1.1..1..1...1...1...1....1....1.....1.....1......1......1.......1.......1

.1.1..2..3...4...5...7...10...14....19....26.....36.....50......69......95

.1.1..3..5...7..10..17...28...43....66...105....168....264.....413.....651

.1.1..4..7..11..18..34...59..100...174...309....538....930....1620....2835

.1.1..5.10..18..32..62..118..227...439...839...1592...3037....5823...11144

.1.1..7.17..34..62.148..347..786..1702..3761...8400..18843...41959...93233

.1.1.10.28..59.118.347..960.2418..5862.15035..39090.100159..253642..646112

.1.1.14.43.100.227.786.2418.6802.18758.55226.162010.467274.1341081.3887275

Links

R. H. Hardin, Table of n, a(n) for n = 1..449

Formula

Empirical for column k:

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

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

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

k=4: a(n) = a(n-1) +2*a(n-4) +a(n-7)

k=5: a(n) = a(n-1) +3*a(n-4) +a(n-6) +3*a(n-7) +a(n-10)

k=6: a(n) = a(n-1) +4*a(n-4) +a(n-5) +3*a(n-6) +6*a(n-7) +2*a(n-9) +4*a(n-10) +a(n-13)

Example

Some solutions for n=7 k=4
..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..1..1
..0..0..0..0. .0..1..1..1. .0..0..0..0. .0..1..1..0. .0..1..1..1
..0..0..0..0. .0..1..1..0. .0..0..0..0. .1..1..1..0. .0..1..1..0
..0..0..0..0. .0..0..0..0. .0..0..1..1. .1..1..0..0. .0..0..0..0
..0..1..1..0. .0..0..1..1. .0..1..1..1. .0..0..1..1. .0..1..1..0
..1..1..1..0. .0..1..1..1. .0..1..1..0. .0..1..1..1. .1..1..1..0
..1..1..0..0. .0..1..1..0. .0..0..0..0. .0..1..1..0. .1..1..0..0

Crossrefs

Column 3 is A003269(n+2).

Sequence in context: A260222 A181386 A193517 * A327482 A189006 A245013

Adjacent sequences: A296551 A296552 A296553 * A296555 A296556 A296557

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 15 2017

Status

approved