A300040 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4, 6, 7 or 8 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, 766231, 486305, 128610, 10622, 21, 34, 38809, 758715, 4532025, 11576060

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......766231......11576060.......173419447

..5...793...21792....486305....11576060.....281861630......6789384478

..8..2907..128610...4532025...173419447....6789384478....262361247480

.13.10622..758715..42210111..2597671575..163627792463..10149632583491

.21.38809.4478515.393354513.38941599079.3947880819311.393165011518395

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..0..1. .0..1..1..0. .0..1..0..1. .0..0..0..1. .0..0..0..0
..1..0..1..0. .1..0..1..0. .1..0..1..1. .1..0..1..0. .0..1..0..1
..1..1..1..0. .0..1..0..0. .1..0..0..1. .1..0..1..0. .0..1..0..1
..0..0..0..1. .1..0..1..1. .1..1..1..0. .1..0..1..1. .0..1..0..1
..1..1..0..0. .0..0..1..1. .1..0..0..1. .0..1..0..1. .1..0..0..1

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297917.

Column 3 is A299223.

Column 4 is A299224.

Sequence in context: A298337 A299398 A299228 * A206359 A297951 A298560

Adjacent sequences: A300037 A300038 A300039 * A300041 A300042 A300043

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 23 2018

Status

approved