A299228 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 4, 1, 2, 17, 17, 2, 3, 61, 113, 61, 3, 5, 216, 628, 628, 216, 5, 8, 793, 3669, 5663, 3669, 793, 8, 13, 2907, 21792, 51862, 51862, 21792, 2907, 13, 21, 10622, 128610, 486305, 766094, 486305, 128610, 10622, 21, 34, 38809, 758715, 4532025, 11568483

Offset

1,5

Comments

Table starts

..0.....1.......1.........2...........3.............5...............8

..1.....4......17........61.........216...........793............2907

..1....17.....113.......628........3669.........21792..........128610

..2....61.....628......5663.......51862........486305.........4532025

..3...216....3669.....51862......766094......11568483.......173234478

..5...793...21792....486305....11568483.....281251424......6766315496

..8..2907..128610...4532025...173234478....6766315496....260938102438

.13.10622..758715..42210111..2594065569..162902164724..10077166692402

.21.38809.4478515.393354513.38873368814.3925885203249.389637415718865

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: [order 14] for n>16

k=4: [order 49] for n>51

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297917.

Sequence in context: A298547 A298337 A299398 * A300040 A206359 A297951

Adjacent sequences: A299225 A299226 A299227 * A299229 A299230 A299231

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 05 2018

Status

approved