A296327 T(n,k) = Number of n X k 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 neighboring 1's.

1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 8, 11, 8, 1, 1, 15, 23, 23, 15, 1, 1, 26, 54, 61, 54, 26, 1, 1, 45, 122, 185, 185, 122, 45, 1, 1, 80, 278, 562, 853, 562, 278, 80, 1, 1, 140, 634, 1677, 3569, 3569, 1677, 634, 140, 1, 1, 245, 1438, 4998, 14691, 20088, 14691, 4998, 1438, 245, 1, 1

Offset: 1

Author

R. H. Hardin, Dec 10 2017

Keywords

• nonn
• tabl

Comments

Table starts

.1...1....1.....1......1.......1........1.........1...........1............1

.1...3....5.....8.....15......26.......45........80.........140..........245

.1...5...11....23.....54.....122......278.......634........1438.........3274

.1...8...23....61....185.....562.....1677......4998.......14968........44818

.1..15...54...185....853....3569....14691.....62193......261763......1099727

.1..26..122...562...3569...20088...112235....643541.....3666933.....20890748

.1..45..278..1677..14691..112235...850404...6660799....51754039....401363520

.1..80..634..4998..62193..643541..6660799..72224019...769931084...8196375877

.1.140.1438.14968.261763.3666933.51754039.769931084.11207386103.163095751500

Examples

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

Links

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

Crossrefs

Column 2 is A193147(n+1).

Formula

Empirical for column k:

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

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

k=3: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) -2*a(n-4) +4*a(n-5) -3*a(n-6) +2*a(n-7) -a(n-8).

k=4: [order 14].

k=5: [order 40].

k=6: [order 83].