A298254 -id:A298254 - cp's OEIS frontend

A298930 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 2, 1, 2, 0, 0, 11, 4, 4, 11, 0, 0, 13, 3, 11, 3, 13, 0, 0, 34, 7, 23, 23, 7, 34, 0, 0, 65, 14, 72, 94, 72, 14, 65, 0, 0, 123, 35, 201, 255, 255, 201, 35, 123, 0, 0, 266, 89, 597, 666, 955, 666, 597, 89, 266, 0, 0, 499, 242, 1717, 2720, 3569, 3569, 2720

Offset: 1

R. H. Hardin, Jan 29 2018

Table starts
.0...0..0....0....0.....0......0.......0........0.........0.........0
.0...1..3....2...11....13.....34......65......123.......266.......499
.0...3..1....4....3.....7.....14......35.......89.......242.......643
.0...2..4...11...23....72....201.....597.....1717......5183.....15479
.0..11..3...23...94...255....666....2720.....8571.....30093....106192
.0..13..7...72..255...955...3569...15031....61046....253624...1067751
.0..34.14..201..666..3569..15163...77576...375845...1886321...9434661
.0..65.35..597.2720.15031..77576..491338..2806944..16889645.100996053
.0.123.89.1717.8571.61046.375845.2806944.19329083.138482223.988954778

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

R. H. Hardin, Table of n, a(n) for n = 1..220

Column 2 is A297870.

Column 3 is A298254.

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4)
k=3: [order 18] for n>19
k=4: [order 60] for n>61

cp's OEIS Frontend

A298930 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

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