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A275401 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2. 13
1, 2, 2, 5, 9, 3, 14, 54, 16, 6, 41, 324, 84, 31, 12, 122, 1944, 444, 178, 63, 24, 365, 11664, 2344, 1011, 394, 129, 48, 1094, 69984, 12376, 5758, 2404, 1017, 260, 96, 3281, 419904, 65344, 32771, 14884, 8122, 2645, 534, 192, 9842, 2519424, 345008, 186538, 91849 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
...1....2.....5......14.......41.......122.........365.........1094
...2....9....54.....324.....1944.....11664.......69984.......419904
...3...16....84.....444.....2344.....12376.......65344.......345008
...6...31...178....1011.....5758.....32771......186538......1061795
..12...63...394....2404....14884.....91849......566331......3495079
..24..129..1017....8122....65045....518049.....4142271.....33102260
..48..260..2645...27373...283169...2940064....30551417....317215507
..96..534..6980...94065..1266905..17159883...232200615...3146508594
.192.1083.18464..323306..5656712.100110527..1766745035..31272546310
.384.2210.48959.1109170.25396322.587134035.13518543301.312946900074
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) for n>3
k=2: [order 9] for n>10
k=3: [order 24] for n>28
k=4: [order 65] for n>69
Empirical for row n:
n=1: a(n) = 4*a(n-1) -3*a(n-2)
n=2: a(n) = 6*a(n-1) for n>2
n=3: a(n) = 4*a(n-1) +6*a(n-2) +4*a(n-3)
n=4: a(n) = 3*a(n-1) +11*a(n-2) +25*a(n-3) +2*a(n-4) -24*a(n-5) for n>6
n=5: [order 9] for n>10
n=6: [order 16] for n>17
n=7: [order 21] for n>22
EXAMPLE
Some solutions for n=4 k=4
..0..1..1..1. .0..0..1..1. .0..0..0..1. .0..1..1..2. .0..1..0..0
..2..2..0..1. .2..2..0..0. .1..2..2..0. .0..0..0..0. .0..2..1..1
..1..2..2..2. .1..2..2..0. .1..1..1..2. .1..2..2..0. .1..2..2..1
..1..0..1..2. .1..1..1..1. .0..0..0..1. .1..1..1..2. .1..1..0..0
CROSSREFS
Column 1 is A003945(n-2).
Row 1 is A007051(n-1).
Sequence in context: A040009 A227527 A275504 * A011273 A274068 A274065
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 26 2016
STATUS
approved

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Last modified May 20 14:08 EDT 2024. Contains 372717 sequences. (Running on oeis4.)