A302427 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 3, 3, 4, 5, 9, 6, 8, 8, 17, 11, 10, 16, 13, 25, 21, 21, 21, 32, 21, 65, 38, 42, 51, 42, 64, 34, 185, 88, 83, 148, 93, 86, 128, 55, 385, 188, 235, 372, 362, 207, 179, 256, 89, 649, 377, 532, 1359, 992, 879, 517, 370, 512, 144, 1489, 735, 1250, 4223, 4231, 2503, 2447

Offset

1,2

Comments

Table starts

...1...2....3....5.....8.....13.....21......34.......55........89........144

...2...3....9...17....25.....65....185.....385......649......1489.......3929

...4...6...11...21....38.....88....188.....377......735......1557.......3288

...8..10...21...42....83....235....532....1250.....2839......6972......16274

..16..21...51..148...372...1359...4223...12765....36991....120577.....379049

..32..42...93..362...992...4231..14764...53851...182216....685166....2496115

..64..86..207..879..2503..12527..48037..204549...775916...3358602...13687791

.128.179..517.2447..7611..49454.227283.1171867..5110314..27366139..134037982

.256.370.1007.6306.21321.179252.940829.6104653.30957683.207165078.1213329113

Links

R. H. Hardin, Table of n, a(n) for n = 1..286

Formula

Empirical for column k:

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

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

k=3: a(n) = a(n-1) +10*a(n-3) -8*a(n-4) for n>9

k=4: [order 42] for n>43

k=5: [order 21] for n>24

Empirical for row n:

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

n=2: a(n) = a(n-1) +16*a(n-4) -8*a(n-5) for n>6

n=3: [order 18] for n>19

n=4: [order 68] for n>69

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240513.

Row 1 is A000045(n+1).

Row 2 is A302164.

Sequence in context: A330265 A302163 A302635 * A303197 A059185 A302309

Adjacent sequences: A302424 A302425 A302426 * A302428 A302429 A302430

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 07 2018

Status

approved