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A275266 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,-1) and new values introduced in order 0..2. 13
1, 2, 2, 5, 9, 5, 14, 54, 24, 14, 41, 324, 128, 64, 41, 122, 1944, 688, 396, 172, 122, 365, 11664, 3728, 2564, 1440, 476, 365, 1094, 69984, 20224, 17036, 13156, 5676, 1320, 1094, 3281, 419904, 109760, 114184, 126420, 73012, 22844, 3672, 3281, 9842 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
....1.....2.......5.......14.........41..........122............365
....2.....9......54......324.......1944........11664..........69984
....5....24.....128......688.......3728........20224.........109760
...14....64.....396.....2564......17036.......114184.........767400
...41...172....1440....13156.....126420......1224088.......11894712
..122...476....5676....73012....1020324.....14005180......194398028
..365..1320...22844...409728....8391716....161725644.....3224773976
.1094..3672...93968..2315520...70863268...1922952988....56045462432
.3281.10220..389820.13124196..603245904..22903224024...981633748272
.9842.28472.1626348.74374784.5149743348.271600215464.17187870741644
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 4*a(n-1) -3*a(n-2)
k=2: [order 9] for n>10
k=3: [order 14] for n>17
k=4: [order 43] for n>47
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) = 6*a(n-1) -2*a(n-2) -6*a(n-3) for n>4
n=4: a(n) = 8*a(n-1) -7*a(n-2) -9*a(n-3) -8*a(n-4) -12*a(n-5) +16*a(n-6) for n>7
n=5: [order 18] for n>19
n=6: [order 24] for n>26
n=7: [order 43] for n>45
EXAMPLE
Some solutions for n=4 k=4
..0..1..2..1. .0..1..0..2. .0..1..2..2. .0..1..2..1. .0..1..0..1
..2..1..2..0. .0..2..0..1. .0..1..0..0. .2..1..2..1. .0..1..0..1
..2..1..0..1. .0..1..0..2. .2..1..0..1. .2..1..0..0. .0..2..0..1
..2..0..2..1. .1..2..0..1. .0..1..2..1. .2..0..0..1. .2..2..0..2
CROSSREFS
Column 1 is A007051(n-1).
Row 1 is A007051(n-1).
Sequence in context: A274068 A274065 A233073 * A223387 A278386 A262614
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 21 2016
STATUS
approved

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Last modified July 23 04:10 EDT 2024. Contains 374544 sequences. (Running on oeis4.)