A303040 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 3, 3, 4, 5, 11, 6, 8, 8, 21, 14, 10, 16, 13, 31, 28, 35, 21, 32, 21, 113, 56, 74, 71, 42, 64, 34, 363, 150, 234, 197, 186, 86, 128, 55, 813, 360, 869, 703, 544, 459, 179, 256, 89, 1751, 828, 2926, 3069, 2494, 1686, 1287, 370, 512, 144, 5001, 1906, 8500, 11079

Offset

1,2

Comments

Table starts

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

...2...3...11....21.....31.....113......363.......813.......1751........5001

...4...6...14....28.....56.....150......360.......828.......1906........4628

...8..10...35....74....234.....869.....2926......8500......27931.......96592

..16..21...71...197....703....3069....11079.....39281.....147655......574771

..32..42..186...544...2494...13597....59654....251705....1186522.....5869222

..64..86..459..1686...9882...63254...345668...1853428...10924077....67726475

.128.179.1287..5252..38855..298328..2060154..13840842..103929273...827923879

.256.370.3490.16336.158630.1487003.13122422.112389422.1107624272.11716920536

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

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: [order 13] for n>16

k=4: [order 70]

Empirical for row n:

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

n=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) +12*a(n-4) -16*a(n-5) for n>6

n=3: [order 11] for n>12

n=4: [order 61] for n>62

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240513.

Row 1 is A000045(n+1).

Row 2 is A302310.

Sequence in context: A303197 A059185 A302309 * A302877 A303525 A368643

Adjacent sequences: A303037 A303038 A303039 * A303041 A303042 A303043

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 17 2018

Status

approved