A198253 - OEIS

A198253

T(n,k)=Number of 2nX2k 0..4 arrays with values 0..4 introduced in row major order and each element equal to exactly two horizontal and vertical neighbors

%I #5 Mar 31 2012 12:36:34

%S 1,1,1,2,5,2,5,40,40,5,15,485,1675,485,15,51,6528,81440,81440,6528,51,

%T 187,90641,4059950,14520192,4059950,90641,187,715,1268648,203087097,

%U 2606019472,2606019472,203087097,1268648,715,2795,17794141,10164141586

%N T(n,k)=Number of 2nX2k 0..4 arrays with values 0..4 introduced in row major order and each element equal to exactly two horizontal and vertical neighbors

%C Table starts

%C .....1.........1............2..............5...............15...............51

%C .....1.........5...........40............485.............6528............90641

%C .....2........40.........1675..........81440..........4059950........203087097

%C .....5.......485........81440.......14520192.......2606019472.....468268681671

%C ....15......6528......4059950.....2606019472....1683040515731.1088857594220452

%C ....51.....90641....203087097...468268681671.1088857594220452

%C ...187...1268648..10164141586.84165911962889

%C ...715..17794141.508740409496

%C ..2795.249720000

%C .11051

%H R. H. Hardin, <a href="/A198253/b198253.txt">Table of n, a(n) for n = 1..60</a>

%e Some solutions for n=5 k=3

%e ..0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0

%e ..0..1..1..2..2..0....0..1..1..2..2..0....0..1..1..2..2..0....0..1..1..2..2..0

%e ..0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..3..3..0....0..3..3..0..0..0

%e ..3..3..4..4..3..3....3..3..3..3..4..4....1..1..0..3..3..0....0..3..3..0..4..4

%e ..3..3..4..4..3..3....3..0..0..3..4..4....1..1..0..0..0..0....0..0..0..0..4..4

%e ..4..4..0..0..4..4....3..0..0..3..0..0....4..4..3..3..2..2....3..3..1..1..2..2

%e ..4..4..0..0..4..4....3..3..3..3..0..0....4..4..3..3..2..2....3..3..1..1..2..2

%e ..0..0..1..1..3..3....2..2..4..4..1..1....0..0..4..4..3..3....1..1..2..2..0..0

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_ Oct 22 2011