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A200801 T(n,k) is the number of n X k 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

%I A200801 #12 Oct 14 2024 18:18:26
%S A200801 1,2,2,5,15,5,15,178,178,15,51,2614,9880,2614,51,187,40148,583813,
%T A200801 583813,40148,187,715,622645,34679839,132636590,34679839,622645,715,
%U A200801 2795,9676364,2060918000,30147154218,30147154218,2060918000,9676364,2795
%N A200801 T(n,k) is the number of n X k 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.
%H A200801 Ron Hardin, <a href="/A200801/b200801.txt">Table of n, a(n) for n = 1..97</a>
%e A200801 Table starts:
%e A200801 .....1...........2.................5......................15
%e A200801 .....2..........15...............178....................2614
%e A200801 .....5.........178..............9880..................583813
%e A200801 ....15........2614............583813...............132636590
%e A200801 ....51.......40148..........34679839.............30147154218
%e A200801 ...187......622645........2060918000...........6852264918471
%e A200801 ...715.....9676364......122478253815........1557479347400065
%e A200801 ..2795...150442627.....7278777317468......354005859128023982
%e A200801 .11051..2339207390...432571571252989....80463441477635545163
%e A200801 .43947.36372631268.25707362563355693.18288865135614195620421
%e A200801 ...
%e A200801 Some solutions for n=5 and k=3:
%e A200801 ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
%e A200801 ..0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0
%e A200801 ..2..0..0....0..1..1....0..0..2....2..2..0....2..2..0....2..2..0....2..1..2
%e A200801 ..2..3..3....1..0..2....3..1..0....1..1..1....3..2..2....0..0..1....0..1..3
%e A200801 ..2..2..0....3..2..1....3..3..0....2..2..1....3..1..3....1..1..1....1..1..2
%Y A200801 Main diagonal is A200794.
%Y A200801 Columns 1..7 are A007581(n-1), A200795, A200796, A200797, A200798, A200799, A200780.
%Y A200801 Cf. A199655, A198528.
%K A200801 nonn,tabl
%O A200801 1,2
%A A200801 _R. H. Hardin_, Nov 22 2011