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A268789 T(n,k)=Number of nXk binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once. 8
0, 1, 1, 2, 5, 2, 5, 17, 17, 5, 10, 48, 72, 48, 10, 20, 131, 302, 302, 131, 20, 38, 338, 1144, 1714, 1144, 338, 38, 71, 850, 4207, 9085, 9085, 4207, 850, 71, 130, 2091, 14984, 46195, 67100, 46195, 14984, 2091, 130, 235, 5061, 52335, 228384, 477128, 477128, 228384 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Table starts

...0.....1......2........5........10..........20............38.............71

...1.....5.....17.......48.......131.........338...........850...........2091

...2....17.....72......302......1144........4207.........14984..........52335

...5....48....302.....1714......9085.......46195........228384........1105510

..10...131...1144.....9085.....67100......477128.......3295246.......22302699

..20...338...4207....46195....477128.....4725018......45515227......429442918

..38...850..14984...228384...3295246....45515227.....611932378.....8057509992

..71..2091..52335..1105510..22302699...429442918....8057509992...148013550916

.130..5061.179854..5267662.148575958..3988796543..104456486696..2677312316674

.235.12095.610504.24786180.977609634.36591758790.1337467436839.47829470133134

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) -2*a(n-3) -6*a(n-4) -4*a(n-5) -a(n-6)

k=3: [order 10]

k=4: [order 16]

k=5: [order 26]

k=6: [order 42]

k=7: [order 68]

EXAMPLE

Some solutions for n=4 k=4

..0..0..0..0. .1..0..1..0. .1..0..1..0. .1..1..0..0. .1..1..0..0

..1..0..1..0. .0..0..0..0. .0..1..0..0. .0..0..0..0. .0..0..0..1

..0..0..0..1. .1..0..0..1. .0..0..0..1. .0..0..0..1. .0..0..0..0

..0..1..0..1. .0..0..1..0. .1..0..0..0. .0..0..0..0. .1..0..0..0

CROSSREFS

Column 1 is A001629.

Sequence in context: A166376 A089122 A321577 * A269920 A240706 A240642

Adjacent sequences:  A268786 A268787 A268788 * A268790 A268791 A268792

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 13 2016

STATUS

approved

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Last modified May 25 11:27 EDT 2020. Contains 334592 sequences. (Running on oeis4.)