A268750 T(n,k)=Number of nXk binary arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

2, 4, 4, 7, 11, 7, 13, 32, 32, 13, 23, 89, 143, 89, 23, 41, 244, 623, 623, 244, 41, 72, 659, 2615, 4110, 2615, 659, 72, 126, 1760, 10830, 26334, 26334, 10830, 1760, 126, 219, 4657, 44067, 165019, 255651, 165019, 44067, 4657, 219, 379, 12228, 177429, 1016807

Offset: 1

Author

R. H. Hardin, Feb 12 2016

Keywords

• nonn
• tabl

Comments

Table starts

...2.....4.......7........13..........23............41.............72

...4....11......32........89.........244...........659...........1760

...7....32.....143.......623........2615.........10830..........44067

..13....89.....623......4110.......26334........165019........1016807

..23...244....2615.....26334......255651.......2425799.......22577073

..41...659...10830....165019.....2425799......34732937......487682438

..72..1760...44067...1016807....22577073.....487682438....10319681062

.126..4657..177429...6183665...207252725....6746117783...215027310572

.219.12228..707163..37209717..1880654551...92215499119..4425392044505

.379.31899.2796840.221970102.16909709308.1248437108837.90177748184504

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1404

Crossrefs

Column 1 is A208354(n+1).

Formula

Empirical for column k:

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

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

k=3: a(n) = 4*a(n-1) +8*a(n-2) -24*a(n-3) -38*a(n-4) +4*a(n-5) +12*a(n-6) -a(n-8)

k=4: [order 10]

k=5: [order 18]

k=6: [order 22]

k=7: [order 42]