A208428 -id:A208428 - cp's OEIS frontend

A275565 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,0) (-1,2) or (0,-2) and new values introduced in order 0..2.

1, 2, 2, 3, 14, 3, 6, 36, 54, 6, 12, 96, 126, 216, 12, 24, 288, 294, 504, 864, 24, 48, 864, 672, 1176, 1872, 3456, 48, 96, 2592, 1536, 3192, 4056, 7200, 13824, 96, 192, 7776, 3552, 8664, 13104, 15000, 27360, 55296, 192, 384, 23328, 8214, 23712, 42336, 57600

Offset: 1

R. H. Hardin, Aug 01 2016

Table starts
...1......2.......3.......6.......12........24.........48..........96
...2.....14......36......96......288.......864.......2592........7776
...3.....54.....126.....294......672......1536.......3552........8214
...6....216.....504....1176.....3192......8664......23712.......64896
..12....864....1872....4056....13104.....42336.....138600......453750
..24...3456....7200...15000....57600....221184.....867456.....3402054
..48..13824...27360...54150...248520...1140576....5360184....25190406
..96..55296..104256..196566..1075140...5880600...33275880...188294424
.192.221184..397440..714150..4663710..30456054..206892990..1405458150
.384.884736.1513728.2589894.20186982.157347846.1286374716.10516571736

			Some solutions for n=4 k=4
..0..1..2..2. .0..1..1..2. .0..1..2..2. .0..1..2..0. .0..1..2..0
..1..0..0..1. .0..1..2..0. .1..0..0..2. .0..1..1..2. .1..1..2..2
..2..2..1..1. .1..2..2..1. .1..0..0..1. .2..0..1..1. .1..0..0..2
..2..2..1..0. .1..0..0..1. .2..2..1..1. .2..2..0..1. .2..0..0..1

R. H. Hardin, Table of n, a(n) for n = 1..286

Column 1 is A003945(n-2).
Column 2 is A208428.
Row 1 is A003945(n-2).

Empirical for column k:
k=1: a(n) = 2*a(n-1) for n>3
k=2: a(n) = 4*a(n-1) for n>3
k=3: a(n) = 2*a(n-1) +8*a(n-2) -16*a(n-4) for n>5
k=4: [order 10] for n>11
k=5: [order 32] for n>34
k=6: [order 35] for n>37
Empirical for row n:
n=1: a(n) = 2*a(n-1) for n>3
n=2: a(n) = 3*a(n-1) for n>4
n=3: a(n) = 3*a(n-1) -5*a(n-3) +a(n-4) +7*a(n-5) -5*a(n-6) +2*a(n-8) -a(n-9) for n>10
n=4: [order 25] for n>28
n=5: [order 63] for n>66

A275352 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,-2) and new values introduced in order 0..2.

Original entry on oeis.org

1, 2, 2, 5, 14, 5, 14, 81, 54, 14, 41, 486, 288, 216, 41, 122, 2916, 1536, 1024, 864, 122, 365, 17496, 8192, 6156, 4100, 3456, 365, 1094, 104976, 43712, 38256, 31536, 16956, 13824, 1094, 3281, 629856, 235072, 239112, 266116, 175152, 70272, 55296, 3281

Offset: 1

R. H. Hardin, Jul 24 2016

Table starts
....1......2.......5........14..........41..........122............365
....2.....14......81.......486........2916........17496.........104976
....5.....54.....288......1536........8192........43712.........235072
...14....216....1024......6156.......38256.......239112........1530060
...41....864....4100.....31536......266116......2292520.......20917472
..122...3456...16956....175152.....2130176.....26615196......351504904
..365..13824...70272....982152....17258544....306863916.....5814135340
.1094..55296..291320...5645376...142784608...3682615020...101593710948
.3281.221184.1211092..33154200..1211010160..45094867336..1804283175916
.9842.884736.5070832.197081664.10285035212.548546009720.31575745629020

			Some solutions for n=4 k=4
..0..1..0..2. .0..1..1..2. .0..1..0..0. .0..1..1..1. .0..1..2..1
..1..0..1..0. .2..2..2..0. .1..2..2..0. .1..2..2..0. .0..2..1..2
..0..2..0..1. .0..2..0..0. .2..2..2..1. .2..2..0..0. .0..1..2..0
..2..2..1..0. .0..1..1..1. .0..0..1..1. .0..0..1..1. .0..2..1..0

R. H. Hardin, Table of n, a(n) for n = 1..180

Column 1 is A007051(n-1).
Column 2 is A208428.
Row 1 is A007051(n-1).

Empirical for column k:
k=1: a(n) = 4*a(n-1) -3*a(n-2)
k=2: a(n) = 4*a(n-1) for n>3
k=3: [order 17] for n>20
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>3
n=3: [order 18] for n>20
n=4: [order 41] for n>43

cp's OEIS Frontend

A275565 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,0) (-1,2) or (0,-2) and new values introduced in order 0..2.

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