A297338 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 0 or 2 neighboring 1s.

2, 3, 4, 5, 8, 8, 8, 22, 21, 16, 13, 53, 96, 55, 32, 21, 134, 334, 421, 144, 64, 34, 333, 1310, 2119, 1847, 377, 128, 55, 833, 4888, 13067, 13428, 8105, 987, 256, 89, 2078, 18604, 73147, 130297, 85065, 35568, 2584, 512, 144, 5190, 70255, 427900, 1091456, 1299649

Offset

1,1

Comments

Table starts

...2....3......5........8.........13..........21............34..............55

...4....8.....22.......53........134.........333...........833............2078

...8...21.....96......334.......1310........4888.........18604...........70255

..16...55....421.....2119......13067.......73147........427900.........2455970

..32..144...1847....13428.....130297.....1091456.......9831967........85542000

..64..377...8105....85065....1299649....16277492.....225944546......2976461197

.128..987..35568...538819...12964224...242728633....5193690642....103574723331

.256.2584.156089..3412881..129324245..3619361855..119391166963...3603917287497

.512.6765.684994.21617001.1290083201.53967869192.2744583368968.125396477316407

Links

R. H. Hardin, Table of n, a(n) for n = 1..574

Formula

Empirical for column k:

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

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

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

k=4: a(n) = 8*a(n-1) -10*a(n-2) -4*a(n-3) +3*a(n-4) +a(n-5)

k=5: [order 7] for n>8

k=6: [order 13] for n>14

k=7: [order 20] for n>22

Empirical for row n:

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

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

n=3: [order 12]

n=4: [order 31]

n=5: [order 82]

Example

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

Crossrefs

Column 1 is A000079.

Column 2 is A001906(n+1).

Row 1 is A000045(n+2).

Sequence in context: A164339 A275465 A185198 * A297457 A297694 A297637

Adjacent sequences: A297335 A297336 A297337 * A297339 A297340 A297341

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 28 2017

Status

approved