A296128 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 2 or 5 king-move neighboring 1s.

1, 1, 1, 1, 5, 1, 1, 9, 9, 1, 1, 13, 18, 13, 1, 1, 33, 30, 30, 33, 1, 1, 69, 107, 74, 107, 69, 1, 1, 121, 265, 287, 287, 265, 121, 1, 1, 253, 553, 841, 2098, 841, 553, 253, 1, 1, 529, 1505, 2463, 9344, 9344, 2463, 1505, 529, 1, 1, 1013, 3852, 7953, 35733, 54286, 35733, 7953

Offset: 1

Author

R. H. Hardin, Dec 05 2017

Keywords

• nonn
• tabl

Comments

Table starts

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

.1...5....9....13.....33.......69.......121........253.........529.........1013

.1...9...18....30....107......265.......553.......1505........3852.........8922

.1..13...30....74....287......841......2463.......7953.......24428........74660

.1..33..107...287...2098.....9344.....35733.....182881......859151......3752449

.1..69..265...841...9344....54286....263489....1867837....11720327.....67180741

.1.121..553..2463..35733...263489...1810441...16855693...138016847...1087543621

.1.253.1505..7953.182881..1867837..16855693..227074899..2614792001..28292082465

.1.529.3852.24428.859151.11720327.138016847.2614792001.41069612676.599261543598

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..287

Crossrefs

Column 2 is A089977(n+1).

Column 3 is A183444.

Formula

Empirical for column k:

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

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

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

k=4: [order 9]

k=5: [order 39]