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

1,5

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

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) +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].

Example

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

Crossrefs

Column 2 is A193147(n+1).

Sequence in context: A228356 A253670 A137897 * A347970 A296541 A056152

Adjacent sequences: A296324 A296325 A296326 * A296328 A296329 A296330

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 10 2017

Status

approved