A239155 - OEIS

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 #6 Jul 23 2025 10:57:46

%S 1,2,1,7,2,7,24,7,55,17,88,24,868,208,96,328,88,12159,5775,2778,340,

%T 1235,328,175471,135766,209839,17050,1639,4668,1235,2519488,3313304,

%U 12844591,2709568,166531,6623,17675,4668,36221263,80240064,821135900,330311070

%N 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 Table starts

%C ....1.......2..........7...........24..............88................328

%C ....7......55........868........12159..........175471............2519488

%C ...17.....208.......5775.......135766.........3313304...........80240064

%C ...96....2778.....209839.....12844591.......821135900........52019283568

%C ..340...17050....2709568....330311070.....42600989632......5427557363908

%C .1639..166531...63961519..18120156500...5469574400477...1628795409782566

%C .6623.1221727.1049404191.629468400383.407538214264758.259498303698165490

%H R. H. Hardin, <a href="/A239155/b239155.txt">Table of n, a(n) for n = 1..113</a>

%F Empirical for column k:

%F 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 k=2: [order 14]

%F k=3: [order 9]

%F Empirical for row n:

%F n=1: a(n) = 4*a(n-1) +a(n-2) -6*a(n-3) -3*a(n-4)

%F n=2: a(n) = 4*a(n-1) +a(n-2) -6*a(n-3) -3*a(n-4)

%F 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 n=4: [order 14]

%F n=5: [order 57]

%e Some solutions for n=4 k=4

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

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

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

%Y Row 1 and 2 are A221454(n+1)

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Mar 11 2014