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A274895
T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (0,-1) (-1,-1) or (-2,0) and new values introduced in order 0..2.
11
1, 1, 2, 2, 4, 3, 4, 12, 7, 6, 8, 36, 16, 14, 12, 16, 108, 37, 38, 26, 24, 32, 324, 86, 104, 84, 50, 48, 64, 972, 200, 290, 275, 192, 95, 96, 128, 2916, 465, 815, 913, 753, 436, 181, 192, 256, 8748, 1081, 2291, 3064, 3017, 2049, 990, 345, 384, 512, 26244, 2513, 6434, 10337
OFFSET
1,3
COMMENTS
Table starts
...1...1....2.....4......8......16.......32........64........128.........256
...2...4...12....36....108.....324......972......2916.......8748.......26244
...3...7...16....37.....86.....200......465......1081.......2513........5842
...6..14...38...104....290.....815.....2291......6434......18065.......50729
..12..26...84...275....913....3064....10337.....34921.....117975......398560
..24..50..192...753...3017...12217....49697....202749.....828828.....3391310
..48..95..436..2049...9863...48269...237807...1173787....5803040....28746995
..96.181..990..5602..32539..191974..1143185...6843349...41072451...246859250
.192.345.2253.15305.107369..767905..5539989..40156061..292253909..2133745005
.384.657.5121.41866.354366.3065418.26833885.236220817.2086382703.18485204565
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) for n>3
k=2: a(n) = a(n-1) +2*a(n-2) -a(n-4) for n>5
k=3: a(n) = a(n-1) +4*a(n-2) -6*a(n-4) -a(n-5) +4*a(n-6) -a(n-8) for n>10
k=4: [order 16] for n>18
k=5: [order 32] for n>34
k=6: [order 64] for n>66
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>2
n=3: a(n) = 3*a(n-1) -2*a(n-2) +a(n-3)
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>6
n=5: [order 8] for n>9
n=6: [order 13] for n>14
n=7: [order 21] for n>22
EXAMPLE
Some solutions for n=4 k=4
..0..1..0..2. .0..1..2..0. .0..1..0..2. .0..1..2..0. .0..1..2..1
..2..1..2..1. .1..2..0..1. .2..1..0..2. .1..2..0..1. .1..2..0..1
..1..0..2..1. .2..0..1..2. .1..0..2..1. .1..2..1..2. .1..0..1..2
..1..0..1..0. .2..0..1..0. .1..0..2..0. .2..0..1..2. .2..0..1..0
CROSSREFS
Column 1 is A003945(n-2).
Column 2 is A052535(n+1).
Row 1 is A000079(n-2).
Row 2 is A003946(n-1).
Row 3 is A010912(n-1).
Sequence in context: A223541 A128181 A125185 * A173387 A133438 A086671
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 10 2016
STATUS
approved