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.

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

R. H. Hardin, Table of n, a(n) for n = 1..611

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

Adjacent sequences: A274855 A274856 A274857 * A274859 A274860 A274861

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 09 2016

Status

approved