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A239155 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

%I A239155 #6 Jul 23 2025 10:57:46
%S A239155 1,2,1,7,2,7,24,7,55,17,88,24,868,208,96,328,88,12159,5775,2778,340,
%T A239155 1235,328,175471,135766,209839,17050,1639,4668,1235,2519488,3313304,
%U A239155 12844591,2709568,166531,6623,17675,4668,36221263,80240064,821135900,330311070
%N A239155 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.
%C A239155 Table starts
%C A239155 ....1.......2..........7...........24..............88................328
%C A239155 ....1.......2..........7...........24..............88................328
%C A239155 ....7......55........868........12159..........175471............2519488
%C A239155 ...17.....208.......5775.......135766.........3313304...........80240064
%C A239155 ...96....2778.....209839.....12844591.......821135900........52019283568
%C A239155 ..340...17050....2709568....330311070.....42600989632......5427557363908
%C A239155 .1639..166531...63961519..18120156500...5469574400477...1628795409782566
%C A239155 .6623.1221727.1049404191.629468400383.407538214264758.259498303698165490
%H A239155 R. H. Hardin, <a href="/A239155/b239155.txt">Table of n, a(n) for n = 1..113</a>
%F A239155 Empirical for column k:
%F A239155 k=1: a(n) = 4*a(n-1) +7*a(n-2) -26*a(n-3) +5*a(n-4) +14*a(n-5)
%F A239155 k=2: [order 14]
%F A239155 k=3: [order 9]
%F A239155 Empirical for row n:
%F A239155 n=1: a(n) = 4*a(n-1) +a(n-2) -6*a(n-3) -3*a(n-4)
%F A239155 n=2: a(n) = 4*a(n-1) +a(n-2) -6*a(n-3) -3*a(n-4)
%F A239155 n=3: a(n) = 14*a(n-1) +14*a(n-2) -124*a(n-3) -6*a(n-4) +90*a(n-5) -27*a(n-6)
%F A239155 n=4: [order 14]
%F A239155 n=5: [order 57]
%e A239155 Some solutions for n=4 k=4
%e A239155 ..0..1..1..0..2....0..1..1..2..3....0..1..2..0..2....0..1..2..0..3
%e A239155 ..0..1..1..0..2....0..1..1..2..3....0..1..2..0..2....0..1..2..0..3
%e A239155 ..0..1..1..0..2....0..2..1..2..1....2..1..2..1..0....0..1..2..0..3
%e A239155 ..0..3..1..3..1....3..2..0..0..1....2..0..1..1..0....1..2..1..2..3
%e A239155 ..0..3..1..3..1....3..2..0..0..1....2..0..1..1..0....1..2..1..2..3
%Y A239155 Row 1 and 2 are A221454(n+1)
%K A239155 nonn,tabl
%O A239155 1,2
%A A239155 _R. H. Hardin_, Mar 11 2014