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A296554 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 3 or 6 neighboring 1s. 6
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified May 18 23:08 EDT 2021. Contains 344008 sequences. (Running on oeis4.)