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A198528 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.

%I A198528 #11 Oct 14 2024 18:06:59
%S A198528 1,2,2,5,15,5,15,193,193,15,52,3660,16714,3660,52,202,81844,1877316,
%T A198528 1877316,81844,202,855,1948672,222590953,1084539825,222590953,1948672,
%U A198528 855,3845,47436498,26670041125,634586561196,634586561196,26670041125
%N A198528 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 A198528 R. H. Hardin, <a href="/A198528/b198528.txt">Table of n, a(n) for n = 1..84</a>
%e A198528 Table starts:
%e A198528 .....1............2...................5......................15
%e A198528 .....2...........15.................193....................3660
%e A198528 .....5..........193...............16714.................1877316
%e A198528 ....15.........3660.............1877316..............1084539825
%e A198528 ....52........81844...........222590953............634586561196
%e A198528 ...202......1948672.........26670041125.........371815743708461
%e A198528 ...855.....47436498.......3201911378187......217885196778717007
%e A198528 ..3845...1163606279.....384557171168810...127683385189755792564
%e A198528 .18002..28617909415...46189600128813487.74824145653256981522691
%e A198528 .86472.704465305625.5547962760669962158
%e A198528 Some solutions for n=6 and k=4:
%e A198528 ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e A198528 ..0..1..1..0....0..1..1..0....0..1..1..0....0..1..1..0....0..1..1..0
%e A198528 ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e A198528 ..2..2..1..2....2..2..1..2....2..2..1..2....2..2..1..2....2..2..1..2
%e A198528 ..2..2..3..2....0..3..1..2....3..0..0..3....2..0..1..0....0..3..4..4
%e A198528 ..1..4..0..4....3..2..4..4....3..1..4..3....1..3..0..0....3..3..0..4
%Y A198528 Main diagonal is A198521.
%Y A198528 Columns 1..7 are A056272, A198522, A198523, A198524, A198525, A198526, A198527.
%Y A198528 Cf. A199655, A200801.
%K A198528 nonn,tabl
%O A198528 1,2
%A A198528 _R. H. Hardin_, Oct 26 2011