|
%I #6 Jan 02 2022 17:20:33
%S 1,1,1,2,5,2,5,28,28,5,14,196,475,196,14,41,1418,8319,8319,1418,41,
%T 122,10314,147231,357943,147231,10314,122,365,75138,2610234,15484811,
%U 15484811,2610234,75138,365,1094,547557,46306024,671539712,1641787181
%N T(n,k) = Number of n X k 0..3 arrays with no element equal to exactly one horizontal or vertical neighbor, with new values 0..3 introduced in row major order.
%C Table starts
%C ....1........1............2..............5...............14................41
%C ....1........5...........28............196.............1418.............10314
%C ....2.......28..........475...........8319...........147231...........2610234
%C ....5......196.........8319.........357943.........15484811.........671539712
%C ...14.....1418.......147231.......15484811.......1641787181......174833637032
%C ...41....10314......2610234......671539712.....174833637032....45829139264557
%C ..122....75138.....46306024....29164866719...18668613617376.12065218512657635
%C ..365...547557....821735065..1267677501494.1996696858027452
%C .1094..3990640..14584690111.55127359226486
%C .3281.29085026.258881423308
%H R. H. Hardin, <a href="/A240774/b240774.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-1) -3*a(n-2) for n>3,
%F k=2: [order 10] for n>11,
%F k=3: [order 34] for n>35.
%e Some solutions for n=3, k=4
%e ..0..1..0..2....0..1..2..1....0..1..2..2....0..1..2..1....0..1..0..2
%e ..1..2..2..3....3..0..1..2....2..3..2..2....3..0..3..0....3..0..2..3
%e ..3..2..2..1....2..3..0..3....3..2..0..1....2..1..0..3....2..1..0..1
%Y Column 1 is A007051(n-2).
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Apr 12 2014
| 