A268781 T(n,k)=Number of nXk 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

1,1

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A208354(n+1).

Diagonal is A143870.

Sequence in context: A265259 A238493 A362937 * A282647 A269089 A282862

Adjacent sequences: A268778 A268779 A268780 * A268782 A268783 A268784

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 13 2016

Status

approved