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A269276
T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.
14
0, 4, 0, 24, 108, 0, 108, 1368, 1620, 0, 432, 13896, 46872, 20412, 0, 1620, 127512, 1104264, 1365336, 236196, 0, 5832, 1104264, 23549400, 74853576, 36673560, 2598156, 0, 20412, 9211608, 474819408, 3719884392, 4684312584, 938176344
OFFSET
1,2
COMMENTS
Table starts
.0........4..........24............108...............432................1620
.0......108........1368..........13896............127512.............1104264
.0.....1620.......46872........1104264..........23549400...........474819408
.0....20412.....1365336.......74853576........3719884392........174924572760
.0...236196....36673560.....4684312584......542973139128......59587625651904
.0..2598156...938176344...279339197256....75556007986536...19356924219624936
.0.27634932.23230366488.16128206816904.10181956012212600.6090616046325570480
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 18*a(n-1) -81*a(n-2)
k=3: a(n) = 42*a(n-1) -441*a(n-2)
k=4: a(n) = 98*a(n-1) -2401*a(n-2) for n>3
k=5: a(n) = 234*a(n-1) -14277*a(n-2) +68796*a(n-3) -86436*a(n-4)
k=6: [order 6] for n>7
k=7: [order 10] for n>11
Empirical for row n:
n=1: a(n) = 6*a(n-1) -9*a(n-2)
n=2: a(n) = 14*a(n-1) -49*a(n-2) for n>4
n=3: a(n) = 36*a(n-1) -378*a(n-2) +972*a(n-3) -729*a(n-4) for n>7
n=4: [order 8] for n>12
n=5: [order 18] for n>23
n=6: [order 40] for n>46
EXAMPLE
Some solutions for n=3 k=4
..0..2..0..1. .0..0..0..0. .0..2..0..0. .0..0..0..0. .0..0..2..0
..0..2..3..1. .2..2..0..0. .2..2..3..1. .2..0..2..1. .0..2..2..3
..2..1..0..2. .3..2..1..1. .0..1..0..2. .0..0..1..3. .3..1..1..0
CROSSREFS
Row 1 is A120908.
Sequence in context: A357810 A057402 A269214 * A359521 A172394 A172395
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 21 2016
STATUS
approved