login
T(n,k) is the number of n X k 0..4 arrays with values 0..4 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.
9

%I #11 Oct 14 2024 18:06:59

%S 1,2,2,5,15,5,15,193,193,15,52,3660,16714,3660,52,202,81844,1877316,

%T 1877316,81844,202,855,1948672,222590953,1084539825,222590953,1948672,

%U 855,3845,47436498,26670041125,634586561196,634586561196,26670041125

%N T(n,k) is the number of n X k 0..4 arrays with values 0..4 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

%H R. H. Hardin, <a href="/A198528/b198528.txt">Table of n, a(n) for n = 1..84</a>

%e Table starts:

%e .....1............2...................5......................15

%e .....2...........15.................193....................3660

%e .....5..........193...............16714.................1877316

%e ....15.........3660.............1877316..............1084539825

%e ....52........81844...........222590953............634586561196

%e ...202......1948672.........26670041125.........371815743708461

%e ...855.....47436498.......3201911378187......217885196778717007

%e ..3845...1163606279.....384557171168810...127683385189755792564

%e .18002..28617909415...46189600128813487.74824145653256981522691

%e .86472.704465305625.5547962760669962158

%e Some solutions for n=6 and k=4:

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

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

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

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

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

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

%Y Main diagonal is A198521.

%Y Columns 1..7 are A056272, A198522, A198523, A198524, A198525, A198526, A198527.

%Y Cf. A199655, A200801.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Oct 26 2011