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A274858
T(n,k) = Number of n X k 0..2 arrays with no element equal to any value at offset (-1,0) (0,-1) or (-2,-2) and new values introduced in order 0..2.
7
1, 1, 1, 2, 3, 2, 4, 9, 9, 4, 8, 27, 19, 27, 8, 16, 81, 43, 43, 81, 16, 32, 243, 100, 118, 100, 243, 32, 64, 729, 233, 330, 330, 233, 729, 64, 128, 2187, 542, 923, 1085, 923, 542, 2187, 128, 256, 6561, 1260, 2585, 3602, 3602, 2585, 1260, 6561, 256, 512, 19683, 2929, 7253
OFFSET
1,4
COMMENTS
Table starts
...1.....1....2.....4......8......16.......32........64........128.........256
...1.....3....9....27.....81.....243......729......2187.......6561.......19683
...2.....9...19....43....100.....233......542......1260.......2929........6809
...4....27...43...118....330.....923.....2585......7253......20368.......57205
...8....81..100...330...1085....3602....12102.....40901.....138307......467309
..16...243..233...923...3602...14414....58775....240587.....983086.....4014830
..32...729..542..2585..12102...58775...289494...1426688....7031552....34766640
..64..2187.1260..7253..40901..240587..1426688...8474549...50615815...304255994
.128..6561.2929.20368.138307..983086..7031552..50615815..367622030..2685052098
.256.19683.6809.57205.467309.4014830.34766640.304255994.2685052098.23768683063
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) for n>2;
k=2: a(n) = 3*a(n-1);
k=3: a(n) = 3*a(n-1) -2*a(n-2) +a(n-3) for n>4;
k=4: a(n) = 5*a(n-1) -9*a(n-2) +10*a(n-3) -6*a(n-4) +a(n-5) for n>7;
k=5: [order 8] for n>10;
k=6: [order 13] for n>15;
k=7: [order 21] for n>24.
EXAMPLE
Some solutions for n=4, k=4
..0..1..0..1. .0..1..0..1. .0..1..2..0. .0..1..2..0. .0..1..2..0
..2..0..1..2. .2..0..1..2. .1..2..0..1. .2..0..1..2. .1..2..0..1
..0..1..2..0. .0..1..2..0. .2..1..2..0. .0..1..2..0. .2..0..1..2
..1..2..0..1. .1..0..1..2. .1..2..0..1. .1..0..1..2. .0..1..2..0
CROSSREFS
Column 1 is A000079(n-2).
Column 2 is A000244(n-1).
Sequence in context: A274749 A247936 A231150 * A207997 A304489 A034800
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 09 2016
STATUS
approved