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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
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
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: A198335 A339050 A296335 * A295051 A295379 A295352
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 17 2017
STATUS
approved