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A296635 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0, 2 or 4 neighboring 1s. 7
2, 3, 3, 5, 8, 5, 8, 19, 19, 8, 13, 47, 71, 47, 13, 21, 116, 260, 260, 116, 21, 34, 286, 966, 1444, 966, 286, 34, 55, 705, 3581, 8042, 8042, 3581, 705, 55, 89, 1738, 13275, 44783, 67488, 44783, 13275, 1738, 89, 144, 4285, 49209, 249329, 565149, 565149, 249329 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

..2....3......5.......8........13..........21...........34.............55

..3....8.....19......47.......116.........286..........705...........1738

..5...19.....71.....260.......966........3581........13275..........49209

..8...47....260....1444......8042.......44783.......249329........1388229

.13..116....966....8042.....67488......565149......4733229.......39643699

.21..286...3581...44783....565149.....7121315.....89713772.....1130293195

.34..705..13275..249329...4733229....89713772...1700240351....32223940011

.55.1738..49209.1388229..39643699..1130293195..32223940011...918770773688

.89.4285.182422.7729475.332039800.14240708558.610746699603.26197140564540

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..311

FORMULA

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

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

k=3: [order 12]

k=4: [order 39]

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+2).

Column 2 is A296329.

Sequence in context: A053218 A198335 A296335 * A295051 A295379 A295352

Adjacent sequences:  A296632 A296633 A296634 * A296636 A296637 A296638

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 17 2017

STATUS

approved

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Last modified May 26 18:08 EDT 2020. Contains 334630 sequences. (Running on oeis4.)