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A275142 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,-2) or (0,-1) and new values introduced in order 0..2. 11
1, 1, 2, 2, 6, 5, 4, 16, 36, 14, 8, 48, 80, 216, 41, 16, 144, 224, 400, 1296, 122, 32, 432, 528, 1088, 2000, 7776, 365, 64, 1296, 1216, 2320, 5248, 10000, 46656, 1094, 128, 3888, 2816, 6464, 9744, 25344, 50000, 279936, 3281, 256, 11664, 6544, 17872, 32384, 41360 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Table starts
....1........1.......2........4........8........16........32.........64
....2........6......16.......48......144.......432......1296.......3888
....5.......36......80......224......528......1216......2816.......6544
...14......216.....400.....1088.....2320......6464.....17872......49792
...41.....1296....2000.....5248.....9744.....32384....107472.....362176
..122.....7776...10000....25344....41360....165568....663904....2695808
..365....46656...50000...122368...175120....841536...4055152...19906560
.1094...279936..250000...590848...741904...4283968..24875600..147762240
.3281..1679616.1250000..2852864..3142672..21800000.152379136.1093999424
.9842.10077696.6250000.13774848.13312656.110943552.933805200.8109111360
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 4*a(n-1) -3*a(n-2)
k=2: a(n) = 6*a(n-1)
k=3: a(n) = 5*a(n-1) for n>2
k=4: a(n) = 4*a(n-1) +4*a(n-2) for n>3
k=5: a(n) = 3*a(n-1) +5*a(n-2) +a(n-3) for n>4
k=6: a(n) = 3*a(n-1) +10*a(n-2) +4*a(n-3) -4*a(n-4) for n>6
k=7: a(n) = 3*a(n-1) +18*a(n-2) +11*a(n-3) -23*a(n-4) -4*a(n-5) for n>7
Empirical for row n:
n=1: a(n) = 2*a(n-1) for n>2
n=2: a(n) = 3*a(n-1) for n>3
n=3: a(n) = 3*a(n-1) -2*a(n-2) +a(n-3) for n>5
n=4: a(n) = 5*a(n-1) -9*a(n-2) +10*a(n-3) -6*a(n-4) +a(n-5) for n>9
n=5: [order 8] for n>12
n=6: [order 13] for n>18
n=7: [order 21] for n>27
EXAMPLE
Some solutions for n=5 k=4
..0..1..2..1. .0..1..0..1. .0..1..0..2. .0..1..2..1. .0..1..2..0
..2..0..1..0. .0..2..1..2. .2..0..1..2. .2..0..2..0. .0..1..2..0
..2..0..1..2. .1..2..1..0. .1..2..1..2. .2..0..1..2. .2..0..2..0
..1..2..0..1. .0..1..2..1. .0..2..0..1. .2..0..1..2. .2..0..1..2
..0..2..0..1. .2..1..2..0. .0..1..2..0. .1..2..0..2. .0..1..0..1
CROSSREFS
Column 1 is A007051(n-1).
Column 2 is A000400(n-1).
Column 3 is A055842.
Row 1 is A000079(n-2).
Sequence in context: A181661 A144160 A368228 * A200226 A300628 A115255
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 17 2016
STATUS
approved

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Last modified April 22 10:51 EDT 2024. Contains 371897 sequences. (Running on oeis4.)