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A241328 T(n,k)=Number of nXk 0..3 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order.

%I A241328 #6 Jul 23 2025 11:12:35
%S A241328 1,1,2,2,8,5,5,59,85,15,14,530,2344,1030,51,41,4877,68935,95144,13011,
%T A241328 187,122,45057,2034543,8949808,3875244,165924,715,365,416533,60066019,
%U A241328 842185933,1162535788,157912026,2121033,2795,1094,3851085,1773370241
%N A241328 T(n,k)=Number of nXk 0..3 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order.
%C A241328 Table starts
%C A241328 ...1.......1..........2..............5................14....................41
%C A241328 ...2.......8.........59............530..............4877.................45057
%C A241328 ...5......85.......2344..........68935...........2034543..............60066019
%C A241328 ..15....1030......95144........8949808.........842185933...........79254376889
%C A241328 ..51...13011....3875244.....1162535788......348722168314.......104609549355169
%C A241328 .187..165924..157912026...151022716125...144410575985227....138095118530911728
%C A241328 .715.2121033.6435036610.19619065042282.59802363257355728.182299462522915741748
%H A241328 R. H. Hardin, <a href="/A241328/b241328.txt">Table of n, a(n) for n = 1..112</a>
%F A241328 Empirical for column k:
%F A241328 k=1: a(n) = 7*a(n-1) -14*a(n-2) +8*a(n-3)
%F A241328 k=2: [order 9] for n>10
%F A241328 k=3: [order 15]
%F A241328 k=4: [order 53]
%F A241328 Empirical for row n:
%F A241328 n=1: a(n) = 4*a(n-1) -3*a(n-2) for n>3
%F A241328 n=2: a(n) = 12*a(n-1) -26*a(n-2) +2*a(n-3) +28*a(n-4) -6*a(n-5) -9*a(n-6) for n>8
%F A241328 n=3: [order 11] for n>13
%F A241328 n=4: [order 36] for n>38
%e A241328 Some solutions for n=3 k=4
%e A241328 ..0..1..0..1....0..1..2..1....0..1..2..1....0..1..0..2....0..1..0..1
%e A241328 ..1..0..1..2....1..0..2..3....0..2..3..0....1..2..0..1....2..0..3..2
%e A241328 ..1..0..3..0....0..2..0..1....1..3..2..3....3..2..1..3....3..1..2..0
%Y A241328 Column 1 is A007581(n-1)
%Y A241328 Row 1 is A007051(n-2)
%K A241328 nonn,tabl
%O A241328 1,3
%A A241328 _R. H. Hardin_, Apr 19 2014