A268781 T(n,k) = Number of n X k binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two no more than once.

2, 4, 4, 7, 11, 7, 13, 26, 26, 13, 23, 65, 91, 65, 23, 41, 148, 316, 316, 148, 41, 72, 343, 1031, 1462, 1031, 343, 72, 126, 766, 3354, 6383, 6383, 3354, 766, 126, 219, 1709, 10615, 27531, 38483, 27531, 10615, 1709, 219, 379, 3752, 33344, 115391, 224960

Offset: 1

Author

R. H. Hardin, Feb 13 2016

Keywords

• nonn
• tabl

Comments

Table starts

...2....4......7......13........23.........41...........72...........126

...4...11.....26......65.......148........343..........766..........1709

...7...26.....91.....316......1031.......3354........10615.........33344

..13...65....316....1462......6383......27531.......115391........478849

..23..148...1031....6383.....38483.....224960......1288693.......7271509

..41..343...3354...27531....224960....1755113.....13493468.....101738555

..72..766..10615..115391...1288693...13493468....140404442....1425678976

.126.1709..33344..478849...7271509..101738555...1425678976...19400886875

.219.3752.103339.1957904..40511381..758303322..14341399141..262072220011

.379.8195.317958.7940136.223527424.5590121407.142487073304.3491534799847

Examples

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

Links

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

Crossrefs

Column 1 is A208354(n+1).

Diagonal is A143870.

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

k=3: a(n) = 4*a(n-1) +2*a(n-2) -16*a(n-3) -a(n-4) +12*a(n-5) -4*a(n-6).

k=4: [order 8].

k=5: [order 12].

k=6: [order 16].

k=7: [order 28].