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A269214
T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.
13
0, 4, 0, 24, 96, 0, 108, 768, 1152, 0, 432, 6528, 18048, 11424, 0, 1620, 49536, 308544, 361728, 103488, 0, 5832, 360960, 4744704, 12548544, 6712704, 889056, 0, 20412, 2546304, 70371048, 394072704, 474091776, 118872576, 7375872, 0, 69984, 17563392
OFFSET
1,2
COMMENTS
Table starts
.0........4..........24............108...............432................1620
.0.......96.........768...........6528.............49536..............360960
.0.....1152.......18048.........308544...........4744704............70371048
.0....11424......361728.......12548544.........394072704.........11985002256
.0...103488.....6712704......474091776.......30541426560.......1910809190712
.0...889056...118872576....17118725376.....2267772823680.....292321215814512
.0..7375872..2039727744...599456856000...163535201141376...43468685827935816
.0.59698464.34214296320.20531285093184.11544796423498368.6331185189881558208
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 14*a(n-1) -49*a(n-2) for n>3
k=3: a(n) = 30*a(n-1) -237*a(n-2) +180*a(n-3) -36*a(n-4) for n>5
k=4: [order 6] for n>7
k=5: [order 20] for n>21
k=6: [order 42] for n>43
Empirical for row n:
n=1: a(n) = 6*a(n-1) -9*a(n-2)
n=2: a(n) = 10*a(n-1) -13*a(n-2) -60*a(n-3) -36*a(n-4)
n=3: [order 8]
n=4: [order 20]
n=5: [order 52] for n>53
EXAMPLE
Some solutions for n=3 k=4
..2..2..3..2. .2..2..2..3. .0..1..0..2. .0..0..0..2. .2..2..0..0
..0..2..0..2. .0..0..1..0. .1..1..3..0. .0..1..2..0. .0..0..2..3
..2..1..0..1. .0..1..0..1. .0..1..0..2. .0..0..0..0. .0..0..1..3
CROSSREFS
Column 2 is A269091.
Row 1 is A120908.
Sequence in context: A329891 A357810 A057402 * A269276 A359521 A172394
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 20 2016
STATUS
approved